Implied Volatility Rank & Model-Free IVRThis is an update to my previous IV Rank & IV Percentile Script.
I originally made this script for binary/digital options, but this also can be used for vanilla options too.
There are two lines on this script, one plotting Model-Based IV rank and Model-Free IV Rank.
How it works:
Model-Based IV Rank:
1. Take whatever timeframe you're using and multiply it by 252. This is done because typically IV is calculated over a year, which has 252 days. But this can be used for any timeframe, so just multiply you're timeframe by 252. In the picture above I'm using a 30 min chart, so I multiplied 30 min by 252 and got 7 days, 14 hrs , and 30 min.
2. Next input the result you got from step 1 into the corresponding input boxes.
3. Then input the timeframe you are using into the input box labeled timeframe. I'm using 30 min so I put 30.
4.Finally choose the delta that you want to use and input its standard deviation into the input box. There is a list of common deltas and their corresponding standard deviations in the menu so you don't have to go looking them up. Typically 16D or 1 standard deviation is used when calculating IV, but you can choose whichever one you want.
*FYI. For people trading binary/digital options, the delta of a vanilla option is the same as the price of a binary/digital option. This is because the delta is the first-order mathematical derivative of the vanilla option's price, and a binary/digital option is a mathematical derivative of a vanilla option. So when you see the list of deltas and their corresponding standard deviations values, just know that 40D=$40 binary, 30D=$30 binary, 20D=$20 binary, and so on. But again typically the 16D or $16 binary's standard deviation value would be used*
This calculation of IV rank is useful for vanilla option traders who use Tradingview and don't have access to this metric.
This calculation of IV rank is useful for binary/digital option traders using Tradingview because the only two regulated binary options exchanges: the CBOE and Nadex, do not offer advanced options data, such as IV rank. On the CBOE and Nadex only the market-makers have this data, which they get from their own in-house pricing models. So at least now any binary option traders can have the same data as the market makers that they are trading against. Also if your wondering how accurate my pricing model is; just know that I have have compared the prices given by the pricing model to realtime prices on Nadex (live account) and the prices that my model shows for differing strike prices matches the prices that the market-makers set. So the pricing model, upon which this IV rank is based, is accurate.*
Model-Free IV Rank:
This IV Rank is based off the VixFix and just ranks the VixFix's values over the past 252 periods. In the menu you can see the recommended periods for calculating the VixFix, with 22 being the one most people use. This is the exact same methodology used in my original IV Rank script.
Which should you use?
This is up to you and each have their own pros and cons.
The main pro of using the model-free version is that because it does not rely on a pricing model, it does not take as many steps to calculate IV and therefore can update its IV projections much quicker than the model based approach. This is why if you zoom out the model-free version will have a more choppy appearance than the model based.
The main pro of using the model based version is that this is what the overwhelming majority of options traders use, and can be applied to any option delta you want, while the model-free version only calculates IV rank on the 16D aka $16 binary aka 1 standard deviation strike.
Cari dalam skrip untuk "Implied volatility"
Volatility Risk Premium (VRP) 1.0ENGLISH
This indicator (V-R-P) calculates the (one month) Volatility Risk Premium for S&P500 and Nasdaq-100.
V-R-P is the premium hedgers pay for over Realized Volatility for S&P500 and Nasdaq-100 index options.
The premium stems from hedgers paying to insure their portfolios, and manifests itself in the differential between the price at which options are sold (Implied Volatility) and the volatility the S&P500 and Nasdaq-100 ultimately realize (Realized Volatility).
I am using 30-day Implied Volatility (IV) and 21-day Realized Volatility (HV) as the basis for my calculation, as one month of IV is based on 30 calendaristic days and one month of HV is based on 21 trading days.
At first, the indicator appears blank and a label instructs you to choose which index you want the V-R-P to plot on the chart. Use the indicator settings (the sprocket) to choose one of the indices (or both).
Together with the V-R-P line, the indicator will show its one year moving average within a range of +/- 15% (which you can change) for benchmarking purposes. We should consider this range the “normalized” V-R-P for the actual period.
The Zero Line is also marked on the indicator.
Interpretation
When V-R-P is within the “normalized” range, … well... volatility and uncertainty, as it’s seen by the option market, is “normal”. We have a “premium” of volatility which should be considered normal.
When V-R-P is above the “normalized” range, the volatility premium is high. This means that investors are willing to pay more for options because they see an increasing uncertainty in markets.
When V-R-P is below the “normalized” range but positive (above the Zero line), the premium investors are willing to pay for risk is low, meaning they see decreasing uncertainty and risks in the market, but not by much.
When V-R-P is negative (below the Zero line), we have COMPLACENCY. This means investors see upcoming risk as being lower than what happened in the market in the recent past (within the last 30 days).
CONCEPTS:
Volatility Risk Premium
The volatility risk premium (V-R-P) is the notion that implied volatility (IV) tends to be higher than realized volatility (HV) as market participants tend to overestimate the likelihood of a significant market crash.
This overestimation may account for an increase in demand for options as protection against an equity portfolio. Basically, this heightened perception of risk may lead to a higher willingness to pay for these options to hedge a portfolio.
In other words, investors are willing to pay a premium for options to have protection against significant market crashes even if statistically the probability of these crashes is lesser or even negligible.
Therefore, the tendency of implied volatility is to be higher than realized volatility, thus V-R-P being positive.
Realized/Historical Volatility
Historical Volatility (HV) is the statistical measure of the dispersion of returns for an index over a given period of time.
Historical volatility is a well-known concept in finance, but there is confusion in how exactly it is calculated. Different sources may use slightly different historical volatility formulas.
For calculating Historical Volatility I am using the most common approach: annualized standard deviation of logarithmic returns, based on daily closing prices.
Implied Volatility
Implied Volatility (IV) is the market's forecast of a likely movement in the price of the index and it is expressed annualized, using percentages and standard deviations over a specified time horizon (usually 30 days).
IV is used to price options contracts where high implied volatility results in options with higher premiums and vice versa. Also, options supply and demand and time value are major determining factors for calculating Implied Volatility.
Implied Volatility usually increases in bearish markets and decreases when the market is bullish.
For determining S&P500 and Nasdaq-100 implied volatility I used their volatility indices: VIX and VXN (30-day IV) provided by CBOE.
Warning
Please be aware that because CBOE doesn’t provide real-time data in Tradingview, my V-R-P calculation is also delayed, so you shouldn’t use it in the first 15 minutes after the opening.
This indicator is calibrated for a daily time frame.
ESPAŇOL
Este indicador (V-R-P) calcula la Prima de Riesgo de Volatilidad (de un mes) para S&P500 y Nasdaq-100.
V-R-P es la prima que pagan los hedgers sobre la Volatilidad Realizada para las opciones de los índices S&P500 y Nasdaq-100.
La prima proviene de los hedgers que pagan para asegurar sus carteras y se manifiesta en el diferencial entre el precio al que se venden las opciones (Volatilidad Implícita) y la volatilidad que finalmente se realiza en el S&P500 y el Nasdaq-100 (Volatilidad Realizada).
Estoy utilizando la Volatilidad Implícita (IV) de 30 días y la Volatilidad Realizada (HV) de 21 días como base para mi cálculo, ya que un mes de IV se basa en 30 días calendario y un mes de HV se basa en 21 días de negociación.
Al principio, el indicador aparece en blanco y una etiqueta le indica que elija qué índice desea que el V-R-P represente en el gráfico. Use la configuración del indicador (la rueda dentada) para elegir uno de los índices (o ambos).
Junto con la línea V-R-P, el indicador mostrará su promedio móvil de un año dentro de un rango de +/- 15% (que puede cambiar) con fines de evaluación comparativa. Deberíamos considerar este rango como el V-R-P "normalizado" para el período real.
La línea Cero también está marcada en el indicador.
Interpretación
Cuando el V-R-P está dentro del rango "normalizado",... bueno... la volatilidad y la incertidumbre, como las ve el mercado de opciones, es "normal". Tenemos una “prima” de volatilidad que debería considerarse normal.
Cuando V-R-P está por encima del rango "normalizado", la prima de volatilidad es alta. Esto significa que los inversores están dispuestos a pagar más por las opciones porque ven una creciente incertidumbre en los mercados.
Cuando el V-R-P está por debajo del rango "normalizado" pero es positivo (por encima de la línea Cero), la prima que los inversores están dispuestos a pagar por el riesgo es baja, lo que significa que ven una disminución, pero no pronunciada, de la incertidumbre y los riesgos en el mercado.
Cuando V-R-P es negativo (por debajo de la línea Cero), tenemos COMPLACENCIA. Esto significa que los inversores ven el riesgo próximo como menor que lo que sucedió en el mercado en el pasado reciente (en los últimos 30 días).
CONCEPTOS:
Prima de Riesgo de Volatilidad
La Prima de Riesgo de Volatilidad (V-R-P) es la noción de que la Volatilidad Implícita (IV) tiende a ser más alta que la Volatilidad Realizada (HV) ya que los participantes del mercado tienden a sobrestimar la probabilidad de una caída significativa del mercado.
Esta sobreestimación puede explicar un aumento en la demanda de opciones como protección contra una cartera de acciones. Básicamente, esta mayor percepción de riesgo puede conducir a una mayor disposición a pagar por estas opciones para cubrir una cartera.
En otras palabras, los inversores están dispuestos a pagar una prima por las opciones para tener protección contra caídas significativas del mercado, incluso si estadísticamente la probabilidad de estas caídas es menor o insignificante.
Por lo tanto, la tendencia de la Volatilidad Implícita es de ser mayor que la Volatilidad Realizada, por lo cual el V-R-P es positivo.
Volatilidad Realizada/Histórica
La Volatilidad Histórica (HV) es la medida estadística de la dispersión de los rendimientos de un índice durante un período de tiempo determinado.
La Volatilidad Histórica es un concepto bien conocido en finanzas, pero existe confusión sobre cómo se calcula exactamente. Varias fuentes pueden usar fórmulas de Volatilidad Histórica ligeramente diferentes.
Para calcular la Volatilidad Histórica, utilicé el enfoque más común: desviación estándar anualizada de rendimientos logarítmicos, basada en los precios de cierre diarios.
Volatilidad Implícita
La Volatilidad Implícita (IV) es la previsión del mercado de un posible movimiento en el precio del índice y se expresa anualizada, utilizando porcentajes y desviaciones estándar en un horizonte de tiempo específico (generalmente 30 días).
IV se utiliza para cotizar contratos de opciones donde la alta Volatilidad Implícita da como resultado opciones con primas más altas y viceversa. Además, la oferta y la demanda de opciones y el valor temporal son factores determinantes importantes para calcular la Volatilidad Implícita.
La Volatilidad Implícita generalmente aumenta en los mercados bajistas y disminuye cuando el mercado es alcista.
Para determinar la Volatilidad Implícita de S&P500 y Nasdaq-100 utilicé sus índices de volatilidad: VIX y VXN (30 días IV) proporcionados por CBOE.
Precaución
Tenga en cuenta que debido a que CBOE no proporciona datos en tiempo real en Tradingview, mi cálculo de V-R-P también se retrasa, y por este motivo no se recomienda usar en los primeros 15 minutos desde la apertura.
Este indicador está calibrado para un marco de tiempo diario.
Volatility Risk Premium GOLD & SILVER 1.0ENGLISH
This indicator (V-R-P) calculates the (one month) Volatility Risk Premium for GOLD and SILVER.
V-R-P is the premium hedgers pay for over Realized Volatility for GOLD and SILVER options.
The premium stems from hedgers paying to insure their portfolios, and manifests itself in the differential between the price at which options are sold (Implied Volatility) and the volatility GOLD and SILVER ultimately realize (Realized Volatility).
I am using 30-day Implied Volatility (IV) and 21-day Realized Volatility (HV) as the basis for my calculation, as one month of IV is based on 30 calendaristic days and one month of HV is based on 21 trading days.
At first, the indicator appears blank and a label instructs you to choose which index you want the V-R-P to plot on the chart. Use the indicator settings (the sprocket) to choose one of the precious metals (or both).
Together with the V-R-P line, the indicator will show its one year moving average within a range of +/- 15% (which you can change) for benchmarking purposes. We should consider this range the “normalized” V-R-P for the actual period.
The Zero Line is also marked on the indicator.
Interpretation
When V-R-P is within the “normalized” range, … well... volatility and uncertainty, as it’s seen by the option market, is “normal”. We have a “premium” of volatility which should be considered normal.
When V-R-P is above the “normalized” range, the volatility premium is high. This means that investors are willing to pay more for options because they see an increasing uncertainty in markets.
When V-R-P is below the “normalized” range but positive (above the Zero line), the premium investors are willing to pay for risk is low, meaning they see decreasing uncertainty and risks in the market, but not by much.
When V-R-P is negative (below the Zero line), we have COMPLACENCY. This means investors see upcoming risk as being lower than what happened in the market in the recent past (within the last 30 days).
CONCEPTS :
Volatility Risk Premium
The volatility risk premium (V-R-P) is the notion that implied volatility (IV) tends to be higher than realized volatility (HV) as market participants tend to overestimate the likelihood of a significant market crash.
This overestimation may account for an increase in demand for options as protection against an equity portfolio. Basically, this heightened perception of risk may lead to a higher willingness to pay for these options to hedge a portfolio.
In other words, investors are willing to pay a premium for options to have protection against significant market crashes even if statistically the probability of these crashes is lesser or even negligible.
Therefore, the tendency of implied volatility is to be higher than realized volatility, thus V-R-P being positive.
Realized/Historical Volatility
Historical Volatility (HV) is the statistical measure of the dispersion of returns for an index over a given period of time.
Historical volatility is a well-known concept in finance, but there is confusion in how exactly it is calculated. Different sources may use slightly different historical volatility formulas.
For calculating Historical Volatility I am using the most common approach: annualized standard deviation of logarithmic returns, based on daily closing prices.
Implied Volatility
Implied Volatility (IV) is the market's forecast of a likely movement in the price of the index and it is expressed annualized, using percentages and standard deviations over a specified time horizon (usually 30 days).
IV is used to price options contracts where high implied volatility results in options with higher premiums and vice versa. Also, options supply and demand and time value are major determining factors for calculating Implied Volatility.
Implied Volatility usually increases in bearish markets and decreases when the market is bullish.
For determining GOLD and SILVER implied volatility I used their volatility indices: GVZ and VXSLV (30-day IV) provided by CBOE.
Warning
Please be aware that because CBOE doesn’t provide real-time data in Tradingview, my V-R-P calculation is also delayed, so you shouldn’t use it in the first 15 minutes after the opening.
This indicator is calibrated for a daily time frame.
----------------------------------------------------------------------
ESPAŇOL
Este indicador (V-R-P) calcula la Prima de Riesgo de Volatilidad (de un mes) para GOLD y SILVER.
V-R-P es la prima que pagan los hedgers sobre la Volatilidad Realizada para las opciones de GOLD y SILVER.
La prima proviene de los hedgers que pagan para asegurar sus carteras y se manifiesta en el diferencial entre el precio al que se venden las opciones (Volatilidad Implícita) y la volatilidad que finalmente se realiza en el ORO y la PLATA (Volatilidad Realizada).
Estoy utilizando la Volatilidad Implícita (IV) de 30 días y la Volatilidad Realizada (HV) de 21 días como base para mi cálculo, ya que un mes de IV se basa en 30 días calendario y un mes de HV se basa en 21 días de negociación.
Al principio, el indicador aparece en blanco y una etiqueta le indica que elija qué índice desea que el V-R-P represente en el gráfico. Use la configuración del indicador (la rueda dentada) para elegir uno de los metales preciosos (o ambos).
Junto con la línea V-R-P, el indicador mostrará su promedio móvil de un año dentro de un rango de +/- 15% (que puede cambiar) con fines de evaluación comparativa. Deberíamos considerar este rango como el V-R-P "normalizado" para el período real.
La línea Cero también está marcada en el indicador.
Interpretación
Cuando el V-R-P está dentro del rango "normalizado",... bueno... la volatilidad y la incertidumbre, como las ve el mercado de opciones, es "normal". Tenemos una “prima” de volatilidad que debería considerarse normal.
Cuando V-R-P está por encima del rango "normalizado", la prima de volatilidad es alta. Esto significa que los inversores están dispuestos a pagar más por las opciones porque ven una creciente incertidumbre en los mercados.
Cuando el V-R-P está por debajo del rango "normalizado" pero es positivo (por encima de la línea Cero), la prima que los inversores están dispuestos a pagar por el riesgo es baja, lo que significa que ven una disminución, pero no pronunciada, de la incertidumbre y los riesgos en el mercado.
Cuando V-R-P es negativo (por debajo de la línea Cero), tenemos COMPLACENCIA. Esto significa que los inversores ven el riesgo próximo como menor que lo que sucedió en el mercado en el pasado reciente (en los últimos 30 días).
CONCEPTOS :
Prima de Riesgo de Volatilidad
La Prima de Riesgo de Volatilidad (V-R-P) es la noción de que la Volatilidad Implícita (IV) tiende a ser más alta que la Volatilidad Realizada (HV) ya que los participantes del mercado tienden a sobrestimar la probabilidad de una caída significativa del mercado.
Esta sobreestimación puede explicar un aumento en la demanda de opciones como protección contra una cartera de acciones. Básicamente, esta mayor percepción de riesgo puede conducir a una mayor disposición a pagar por estas opciones para cubrir una cartera.
En otras palabras, los inversores están dispuestos a pagar una prima por las opciones para tener protección contra caídas significativas del mercado, incluso si estadísticamente la probabilidad de estas caídas es menor o insignificante.
Por lo tanto, la tendencia de la Volatilidad Implícita es de ser mayor que la Volatilidad Realizada, por lo cual el V-R-P es positivo.
Volatilidad Realizada/Histórica
La Volatilidad Histórica (HV) es la medida estadística de la dispersión de los rendimientos de un índice durante un período de tiempo determinado.
La Volatilidad Histórica es un concepto bien conocido en finanzas, pero existe confusión sobre cómo se calcula exactamente. Varias fuentes pueden usar fórmulas de Volatilidad Histórica ligeramente diferentes.
Para calcular la Volatilidad Histórica, utilicé el enfoque más común: desviación estándar anualizada de rendimientos logarítmicos, basada en los precios de cierre diarios.
Volatilidad Implícita
La Volatilidad Implícita (IV) es la previsión del mercado de un posible movimiento en el precio del índice y se expresa anualizada, utilizando porcentajes y desviaciones estándar en un horizonte de tiempo específico (generalmente 30 días).
IV se utiliza para cotizar contratos de opciones donde la alta Volatilidad Implícita da como resultado opciones con primas más altas y viceversa. Además, la oferta y la demanda de opciones y el valor temporal son factores determinantes importantes para calcular la Volatilidad Implícita.
La Volatilidad Implícita generalmente aumenta en los mercados bajistas y disminuye cuando el mercado es alcista.
Para determinar la Volatilidad Implícita de GOLD y SILVER utilicé sus índices de volatilidad: GVZ y VXSLV (30 días IV) proporcionados por CBOE.
Precaución
Tenga en cuenta que debido a que CBOE no proporciona datos en tiempo real en Tradingview, mi cálculo de V-R-P también se retrasa, y por este motivo no se recomienda usar en los primeros 15 minutos desde la apertura.
Este indicador está calibrado para un marco de tiempo diario.
Options Oscillator [Lite] IVRank, IVx, Call/Put Volatility Skew The first TradingView indicator that provides REAL IVRank, IVx, and CALL/PUT skew data based on REAL option chain for 5 U.S. market symbols.
🔃 Auto-Updating Option Metrics without refresh!
🍒 Developed and maintained by option traders for option traders.
📈 Specifically designed for TradingView users who trade options.
🔶 Ticker Information:
This 'Lite' indicator is currently only available for 5 liquid U.S. market smbols : NASDAQ:TSLA AMEX:DIA NASDAQ:AAPL NASDAQ:AMZN and NYSE:ORCL
🔶 How does the indicator work and why is it unique?
This Pine Script indicator is a complex tool designed to provide various option metrics and visualization tools for options market traders. The indicator extracts raw options data from an external data provider (ORATS), processes and refines the delayed data package using pineseed, and sends it to TradingView, visualizing the data using specific formulas (see detailed below) or interpolated values (e.g., delta distances). This method of incorporating options data into a visualization framework is unique and entirely innovative on TradingView.
The indicator aims to offer a comprehensive view of the current state of options for the implemented instruments, including implied volatility (IV), IV rank (IVR), options skew, and expected market movements, which are objectively measured as detailed below.
The options metrics we display may be familiar to options traders from various major brokerage platforms such as TastyTrade, IBKR, TOS, Tradier, TD Ameritrade, Schwab, etc.
🟨 The following data is displayed in the oscillator 🟨
We use Tastytrade formulas, so our numbers mostly align with theirs!
🔶 𝗜𝗩𝗥𝗮𝗻𝗸
The Implied Volatility Rank (IVR) helps options traders assess the current level of implied volatility (IV) in comparison to the past 52 weeks. IVR is a useful metric to determine whether options are relatively cheap or expensive. This can guide traders on whether to buy or sell options.
IV Rank formula = (current IV - 52 week IV low) / (52 week IV high - 52 week IV low)
IVRank is default blue and you can adjust their settings:
🔶 𝗜𝗩𝘅 𝗮𝘃𝗴
The implied volatility (IVx) shown in the option chain is calculated like the VIX. The Cboe uses standard and weekly SPX options to measure expected S&P 500 volatility. A similar method is used for calculating IVx for each expiration cycle.
We aggregate the IVx values for the 35-70 day monthly expiration cycle, and use that value in the oscillator and info panel.
We always display which expiration the IVx values are averaged for when you hover over the IVx cell.
IVx main color is purple, but you can change the settings:
🔹IVx 5 days change %
We are also displaying the five-day change of the IV Index (IVx value). The IV Index 5-Day Change column provides quick insight into recent expansions or decreases in implied volatility over the last five trading days.
Traders who expect the value of options to decrease might view a decrease in IVX as a positive signal. Strategies such as Strangle and Ratio Spread can benefit from this decrease.
On the other hand, traders anticipating further increases in IVX will focus on the rising IVX values. Strategies like Calendar Spread or Diagonal Spread can take advantage of increasing implied volatility.
This indicator helps traders quickly assess changes in implied volatility, enabling them to make informed decisions based on their trading strategies and market expectations.
Important Note:
The IVx value alone does not provide sufficient context. There are stocks that inherently exhibit high IVx values. Therefore, it is crucial to consider IVx in conjunction with the Implied Volatility Rank (IVR), which measures the IVx relative to its own historical values. This combined view helps in accurately assessing the significance of the IVx in relation to the specific stock's typical volatility behavior.
This indicator offers traders a comprehensive view of implied volatility, assisting them in making informed decisions by highlighting both the absolute and relative volatility measures.
🔶 𝗖𝗔𝗟𝗟/𝗣𝗨𝗧 𝗣𝗿𝗶𝗰𝗶𝗻𝗴 𝗦𝗸𝗲𝘄 𝗵𝗶𝘀𝘁𝗼𝗴𝗿𝗮𝗺
At TanukiTrade, Vertical Pricing Skew refers to the difference in pricing between put and call options with the same expiration date at the same distance (at tastytrade binary expected move). We analyze this skew to understand market sentiment. This is the same formula used by TastyTrade for calculations.
We calculate the interpolated strike price based on the expected move, taking into account the neighboring option prices and their distances. This allows us to accurately determine whether the CALL or PUT options are more expensive.
🔹 What Causes Pricing Skew? The Theory Behind It
The asymmetric pricing of PUT and CALL options is driven by the natural dynamics of the market. The theory is that when CALL options are more expensive than PUT options at the same distance from the current spot price, market participants are buying CALLs and selling PUTs, expecting a faster upward movement compared to a downward one .
In the case of PUT skew, it's the opposite: participants are buying PUTs and selling CALLs , as they expect a potential downward move to happen more quickly than an upward one.
An options trader can take advantage of this phenomenon by leveraging PUT pricing skew. For example, if they have a bullish outlook and both IVR and IVx are high and IV started decreasing, they can capitalize on this PUT skew with strategies like a jade lizard, broken wing butterfly, or short put.
🔴 PUT Skew 🔴
Put options are more expensive than call options, indicating the market expects a faster downward move (▽). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves downward, it could do so faster in velocity compared to a potential upward movement.
🔹 SPY PUT SKEW example:
If AMEX:SPY PUT option prices are 46% higher than CALLs at the same distance for the optimal next monthly expiry (DTE). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves downward, it could do so 46% faster in velocity compared to a potential upward movement
🟢 CALL Skew 🟢
Call options are more expensive than put options, indicating the market expects a faster upward move (△). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves upward, it could do so faster in velocity compared to a potential downward movement.
🔹 INTC CALL SKEW example:
If NASDAQ:INTC CALL option prices are 49% higher than PUTs at the same distance for the optimal next monthly expiry (DTE). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves upward, it could do so 49% faster in velocity compared to a potential downward movement .
🔶 USAGE example:
The script is compatible with our other options indicators.
For example: Since the main metrics are already available in this Options Oscillator, you can hide the main IVR panel of our Options Overlay indicator, freeing up more space on the chart. The following image shows this:
🔶 ADDITIONAL IMPORTANT COMMENTS
🔹 Historical Data:
Yes, we only using historical internal metrics dating back to 2024-07-01, when the TanukiTrade options brand launched. For now, we're using these, but we may expand the historical data in the future.
🔹 What distance does the indicator use to measure the call/put pricing skew?:
It is important to highlight that this oscillator displays the call/put pricing skew changes for the next optimal monthly expiration on a histogram.
The Binary Expected Move distance is calculated using the TastyTrade method for the next optimal monthly expiration: Formula = (ATM straddle price x 0.6) + (1st OTM strangle price x 0.3) + (2nd OTM strangle price x 0.1)
We interpolate the exact difference based on the neighboring strikes at the binary expected move distance using the TastyTrade method, and compare the interpolated call and put prices at this specific point.
🔹 - Why is there a slight difference between the displayed data and my live brokerage data?
There are two reasons for this, and one is beyond our control.
◎ Option-data update frequency:
According to TradingView's regulations and guidelines, we can update external data a maximum of 5 times per day. We strive to use these updates in the most optimal way:
(1st update) 15 minutes after U.S. market open
(2nd, 3rd, 4th updates) 1.5–3 hours during U.S. market open hours
(5th update) 10 minutes before U.S. market close.
You don’t need to refresh your window, our last refreshed data-pack is always automatically applied to your indicator, and you can see the time elapsed since the last update at the bottom of the corner on daily TF.
◎ Brokerage Calculation Differences:
Every brokerage has slight differences in how they calculate metrics like IV and IVx. If you open three windows for TOS, TastyTrade, and IBKR side by side, you will notice that the values are minimally different. We had to choose a standard, so we use the formulas and mathematical models described by TastyTrade when analyzing the options chain and drawing conclusions.
🔹 - EOD data:
The indicator always displays end-of-day (EOD) data for IVR, IV, and CALL/PUT pricing skew. During trading hours, it shows the current values for the ongoing day with each update, and at market close, these values become final. From that point on, the data is considered EOD, provided the day confirms as a closed daily candle.
🔹 - U.S. market only:
Since we only deal with liquid option chains: this option indicator only works for the USA options market and do not include future contracts; we have implemented each selected symbol individually.
Disclaimer:
Our option indicator uses approximately 15min-3 hour delayed option market snapshot data to calculate the main option metrics. Exact realtime option contract prices are never displayed; only derived metrics and interpolated delta are shown to ensure accurate and consistent visualization. Due to the above, this indicator can only be used for decision support; exclusive decisions cannot be made based on this indicator. We reserve the right to make errors.This indicator is designed for options traders who understand what they are doing. It assumes that they are familiar with options and can make well-informed, independent decisions. We work with public data and are not a data provider; therefore, we do not bear any financial or other liability.
Options Oscillator [PRO] IVRank, IVx, Call/Put Volatility Skew𝗧𝗵𝗲 𝗳𝗶𝗿𝘀𝘁 𝗧𝗿𝗮𝗱𝗶𝗻𝗴𝗩𝗶𝗲𝘄 𝗶𝗻𝗱𝗶𝗰𝗮𝘁𝗼𝗿 𝘁𝗵𝗮𝘁 𝗽𝗿𝗼𝘃𝗶𝗱𝗲𝘀 𝗥𝗘𝗔𝗟 𝗜𝗩𝗥𝗮𝗻𝗸, 𝗜𝗩𝘅, 𝗮𝗻𝗱 𝗖𝗔𝗟𝗟/𝗣𝗨𝗧 𝘀𝗸𝗲𝘄 𝗱𝗮𝘁𝗮 𝗯𝗮𝘀𝗲𝗱 𝗼𝗻 𝗥𝗘𝗔𝗟 𝗼𝗽𝘁𝗶𝗼𝗻 𝗰𝗵𝗮𝗶𝗻 𝗳𝗼𝗿 𝗼𝘃𝗲𝗿 𝟭𝟲𝟱+ 𝗺𝗼𝘀𝘁 𝗹𝗶𝗾𝘂𝗶𝗱 𝗨.𝗦. 𝗺𝗮𝗿𝗸𝗲𝘁 𝘀𝘆𝗺𝗯𝗼𝗹𝘀
🔃 Auto-Updating Option Metrics without refresh!
🍒 Developed and maintained by option traders for option traders.
📈 Specifically designed for TradingView users who trade options.
🔶 Ticker Information:
This indicator is currently only available for over 165+ most liquid U.S. market symbols (eg. SP:SPX AMEX:SPY NASDAQ:QQQ NASDAQ:TLT NASDAQ:NVDA , etc.. ), and we are continuously expanding the compatible watchlist here: www.tradingview.com
🔶 How does the indicator work and why is it unique?
This Pine Script indicator is a complex tool designed to provide various option metrics and visualization tools for options market traders. The indicator extracts raw options data from an external data provider (ORATS), processes and refines the delayed data package using pineseed, and sends it to TradingView, visualizing the data using specific formulas (see detailed below) or interpolated values (e.g., delta distances). This method of incorporating options data into a visualization framework is unique and entirely innovative on TradingView.
The indicator aims to offer a comprehensive view of the current state of options for the implemented instruments, including implied volatility (IV), IV rank (IVR), options skew, and expected market movements, which are objectively measured as detailed below.
The options metrics we display may be familiar to options traders from various major brokerage platforms such as TastyTrade, IBKR, TOS, Tradier, TD Ameritrade, Schwab, etc.
🟨 The following data is displayed in the oscillator 🟨
We use Tastytrade formulas, so our numbers mostly align with theirs!
🔶 𝗜𝗩𝗥𝗮𝗻𝗸
The Implied Volatility Rank (IVR) helps options traders assess the current level of implied volatility (IV) in comparison to the past 52 weeks. IVR is a useful metric to determine whether options are relatively cheap or expensive. This can guide traders on whether to buy or sell options.
IV Rank formula = (current IV - 52 week IV low) / (52 week IV high - 52 week IV low)
IVRank is default blue and you can adjust their settings:
🔶 𝗜𝗩𝘅 𝗮𝘃𝗴
The implied volatility (IVx) shown in the option chain is calculated like the VIX. The Cboe uses standard and weekly SPX options to measure expected S&P 500 volatility. A similar method is used for calculating IVx for each expiration cycle.
We aggregate the IVx values for the 35-70 day monthly expiration cycle, and use that value in the oscillator and info panel.
We always display which expiration the IVx values are averaged for when you hover over the IVx cell.
IVx main color is purple, but you can change the settings:
🔹 IVx 5 days change %
We are also displaying the five-day change of the IV Index (IVx value). The IV Index 5-Day Change column provides quick insight into recent expansions or decreases in implied volatility over the last five trading days.
Traders who expect the value of options to decrease might view a decrease in IVX as a positive signal. Strategies such as Strangle and Ratio Spread can benefit from this decrease.
On the other hand, traders anticipating further increases in IVX will focus on the rising IVX values. Strategies like Calendar Spread or Diagonal Spread can take advantage of increasing implied volatility.
This indicator helps traders quickly assess changes in implied volatility, enabling them to make informed decisions based on their trading strategies and market expectations.
Important Note:
The IVx value alone does not provide sufficient context. There are stocks that inherently exhibit high IVx values. Therefore, it is crucial to consider IVx in conjunction with the Implied Volatility Rank (IVR), which measures the IVx relative to its own historical values. This combined view helps in accurately assessing the significance of the IVx in relation to the specific stock's typical volatility behavior.
This indicator offers traders a comprehensive view of implied volatility, assisting them in making informed decisions by highlighting both the absolute and relative volatility measures.
🔶 𝗖𝗔𝗟𝗟/𝗣𝗨𝗧 𝗣𝗿𝗶𝗰𝗶𝗻𝗴 𝗦𝗸𝗲𝘄 𝗵𝗶𝘀𝘁𝗼𝗴𝗿𝗮𝗺
At TanukiTrade, Vertical Pricing Skew refers to the difference in pricing between put and call options with the same expiration date at the same distance (at tastytrade binary expected move). We analyze this skew to understand market sentiment. This is the same formula used by TastyTrade for calculations.
We calculate the interpolated strike price based on the expected move, taking into account the neighboring option prices and their distances. This allows us to accurately determine whether the CALL or PUT options are more expensive.
🔹 What Causes Pricing Skew? The Theory Behind It
The asymmetric pricing of PUT and CALL options is driven by the natural dynamics of the market. The theory is that when CALL options are more expensive than PUT options at the same distance from the current spot price, market participants are buying CALLs and selling PUTs, expecting a faster upward movement compared to a downward one .
In the case of PUT skew, it's the opposite: participants are buying PUTs and selling CALLs , as they expect a potential downward move to happen more quickly than an upward one.
An options trader can take advantage of this phenomenon by leveraging PUT pricing skew. For example, if they have a bullish outlook and both IVR and IVx are high and IV started decreasing, they can capitalize on this PUT skew with strategies like a jade lizard, broken wing butterfly, or short put.
🔴 PUT Skew 🔴
Put options are more expensive than call options, indicating the market expects a faster downward move (▽). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves downward, it could do so faster in velocity compared to a potential upward movement.
🔹 SPY PUT SKEW example:
If AMEX:SPY PUT option prices are 46% higher than CALLs at the same distance for the optimal next monthly expiry (DTE). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves downward, it could do so 46% faster in velocity compared to a potential upward movement
🟢 CALL Skew 🟢
Call options are more expensive than put options, indicating the market expects a faster upward move (△). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves upward, it could do so faster in velocity compared to a potential downward movement.
🔹 INTC CALL SKEW example:
If NASDAQ:INTC CALL option prices are 49% higher than PUTs at the same distance for the optimal next monthly expiry (DTE). This alone doesn't indicate which way the market will move (because nobody knows that), but the options chain pricing suggests that if the market moves upward, it could do so 49% faster in velocity compared to a potential downward movement .
🔶 USAGE example:
The script is compatible with our other options indicators.
For example: Since the main metrics are already available in this Options Oscillator, you can hide the main IVR panel of our Options Overlay indicator, freeing up more space on the chart. The following image shows this:
🔶 ADDITIONAL IMPORTANT COMMENTS
🔹 Historical Data:
Yes, we only using historical internal metrics dating back to 2024-07-01, when the TanukiTrade options brand launched. For now, we're using these, but we may expand the historical data in the future.
🔹 What distance does the indicator use to measure the call/put pricing skew?:
It is important to highlight that this oscillator displays the call/put pricing skew changes for the next optimal monthly expiration on a histogram.
The Binary Expected Move distance is calculated using the TastyTrade method for the next optimal monthly expiration: Formula = (ATM straddle price x 0.6) + (1st OTM strangle price x 0.3) + (2nd OTM strangle price x 0.1)
We interpolate the exact difference based on the neighboring strikes at the binary expected move distance using the TastyTrade method, and compare the interpolated call and put prices at this specific point.
🔹 - Why is there a slight difference between the displayed data and my live brokerage data?
There are two reasons for this, and one is beyond our control.
◎ Option-data update frequency:
According to TradingView's regulations and guidelines, we can update external data a maximum of 5 times per day. We strive to use these updates in the most optimal way:
(1st update) 15 minutes after U.S. market open
(2nd, 3rd, 4th updates) 1.5–3 hours during U.S. market open hours
(5th update) 10 minutes before U.S. market close.
You don’t need to refresh your window, our last refreshed data-pack is always automatically applied to your indicator, and you can see the time elapsed since the last update at the bottom of the corner on daily TF.
◎ Brokerage Calculation Differences:
Every brokerage has slight differences in how they calculate metrics like IV and IVx. If you open three windows for TOS, TastyTrade, and IBKR side by side, you will notice that the values are minimally different. We had to choose a standard, so we use the formulas and mathematical models described by TastyTrade when analyzing the options chain and drawing conclusions.
🔹 - EOD data:
The indicator always displays end-of-day (EOD) data for IVR, IV, and CALL/PUT pricing skew. During trading hours, it shows the current values for the ongoing day with each update, and at market close, these values become final. From that point on, the data is considered EOD, provided the day confirms as a closed daily candle.
🔹 - U.S. market only:
Since we only deal with liquid option chains: this option indicator only works for the USA options market and do not include future contracts; we have implemented each selected symbol individually.
Disclaimer:
Our option indicator uses approximately 15min-3 hour delayed option market snapshot data to calculate the main option metrics. Exact realtime option contract prices are never displayed; only derived metrics and interpolated delta are shown to ensure accurate and consistent visualization. Due to the above, this indicator can only be used for decision support; exclusive decisions cannot be made based on this indicator. We reserve the right to make errors.This indicator is designed for options traders who understand what they are doing. It assumes that they are familiar with options and can make well-informed, independent decisions. We work with public data and are not a data provider; therefore, we do not bear any financial or other liability.
Expected Move BandsExpected Moves
The Expected Move of a security shows the amount that a stock is expected to rise or fall from its current market price based on its level of volatility or implied volatility. The expected move of a stock is usually measured with standard deviations.
An Expected Move Range of 1 SD shows that price will be near the 1 SD range 68% of the time given enough samples.
Expected Move Bands
This indicator gets the Expected Move for 1-4 Standard Deviation Ranges using Historical Volatility. Then it displays it on price as bands.
The Expected Move indicator also allows you to see MTF Expected Moves if you want to.
This indicator calculates the expected price movements by analyzing the historical volatility of an asset. Volatility is the measure of fluctuation.
This script uses log returns for the historical volatility calculation which can be modelled as a normal distribution most of the time meaning it is symmetrical and stationary unlike other scripts that use bands to find "reversals". They are fundamentally incorrect.
What these ranges tell you is basically the odds of the price movement being between these levels.
If you take enough samples, 95.5% of the them will be near the 2nd Standard Deviation. And so on. (The 3rd Standard deviation is 99.7%)
For higher timeframes you might need a smaller sample size.
Features
MTF Option
Parameter customization
Volatility Cone [Loxx]When it comes to forecasting volatility, it seems that the old axiom about weather is applicable: "Everyone talks about it, but no one can do much about it!" Volatility cones are a tool that may be useful in one’s attempt to do something about predicting the future volatility of an asset.
A "volatility cone" is a plot of the range of volatilities within a fixed probability band around the true parameter, as a function of sample length. Volatility cone is a visualization tool for the display of historical volatility term structure. It was introduced by Burghardt and Lane in early 1990 and is popular in the option trading community. This is mostly a static indicator due to processor load and is restricted to the daily time frame.
Why cones?
When we enter the options arena, in an effort to "trade volatility," we want to be able to compare current levels of implied volatility with recent historical volatility in an effort to assess the relative value of the option(s) under consideration Volatility cones can be an effective tool to help us with this assessment. A volatility cone is an analytical application designed to help determine if the current levels of historical or implied volatilities for a given underlying, its options, or any of the new volatility instruments, such as VolContractTM futures, VIX futures, or VXX and VXZ ETNs, are likely to persist in the future. As such, volatility cones are intended to help the user assess the likely volatility that an underlying will go on to display over a certain period. Those who employ volatility cones as a diagnostic tool are relying upon the principle of "reversion to the mean." This means that unusually high levels of volatility are expected to drift or move lower (revert) to their average (mean) levels, while relatively low volatility readings are expected to rise, eventually, to more "normal" values.
How to use
Suppose you want to analyze an options contract expiring in 3-months and this current option has an current implied volatility 25.5%. Suppose also that realized volatility (y-axis) at the 3-month mark (90 on the x-axis) is 45%, median in 35%, the 25th percentile is 30%, and the low is 25%. Comparing this range to the implied volatility you would maybe conclude that this is a relatively "cheap" option contract. To help you visualize implied volatility on the chart given an expiration date in bars, the indicator includes the ability to enter up to three expirations in bars and each expirations current implied volatility
By ascertaining the various historical levels of volatility corresponding to a given time horizon for the options futures under consideration, we’re better prepared to judge the relative "cheapness" or "expensiveness" of the instrument.
Volatility options
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility .
Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.
Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility .
Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.
Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.
The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility. One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility. That drawback is taken into account in the Garman-Klass's volatility estimator.
Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.
Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.
The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.
A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.
Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.
We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility ) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility . It considered being 14 times more efficient than the close-to-close estimator.
Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.
Standard Deviation of Log Returns
This is the simplest calculation of volatility . It's the standard deviation of ln(close/close(1))
Sampling periods used
5, 10, 20, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360
Historical Volatility plot
Purple outer lines: High and low volatility values corresponding to x-axis time
Blue inner lines: 25th and 75th percentiles of volatility corresponding to x-axis time
Green line: Median volatility values corresponding to x-axis time
White dashed line: Realized volatility corresponding to x-axis time
Additional things to know
Due to UI constraints on TradingView it will be easier to visualize this indicator by double-clicking the bottom pane where it appears and then expanded the y- and x-axis to view the entire chart.
You can click on each point on the graph to see what the volatility of that point is.
Option expiration dates will show up as large dots on the graph. You can input your own values in the settings.
Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]Generalized Black-Scholes-Merton Option Pricing Formula is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks aka "Option Sensitivities" and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas".
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm, float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility (vega) when searching for the implied volatility. For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility, al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm, lies between CL and cH. The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility. Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv(i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility, E is the desired degree of accuracy, c(m) is the market price of the option, and dc/dv(i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility).
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Black Scholes Option Pricing Model w/ Greeks [Loxx]The Black Scholes Merton model
If you are new to options I strongly advise you to profit from Robert Shiller's lecture on same . It combines practical market insights with a strong authoritative grasp of key models in option theory. He explains many of the areas covered below and in the following pages with a lot intuition and relatable anecdotage. We start here with Black Scholes Merton which is probably the most popular option pricing framework, due largely to its simplicity and ease in terms of implementation. The closed-form solution is efficient in terms of speed and always compares favorably relative to any numerical technique. The Black–Scholes–Merton model is a mathematical go-to model for estimating the value of European calls and puts. In the early 1970’s, Myron Scholes, and Fisher Black made an important breakthrough in the pricing of complex financial instruments. Robert Merton simultaneously was working on the same problem and applied the term Black-Scholes model to describe new generation of pricing. The Black Scholes (1973) contribution developed insights originally proposed by Bachelier 70 years before. In 1997, Myron Scholes and Robert Merton received the Nobel Prize for Economics. Tragically, Fisher Black died in 1995. The Black–Scholes formula presents a theoretical estimate (or model estimate) of the price of European-style options independently of the risk of the underlying security. Future payoffs from options can be discounted using the risk-neutral rate. Earlier academic work on options (e.g., Malkiel and Quandt 1968, 1969) had contemplated using either empirical, econometric analyses or elaborate theoretical models that possessed parameters whose values could not be calibrated directly. In contrast, Black, Scholes, and Merton’s parameters were at their core simple and did not involve references to utility or to the shifting risk appetite of investors. Below, we present a standard type formula, where: c = Call option value, p = Put option value, S=Current stock (or other underlying) price, K or X=Strike price, r=Risk-free interest rate, q = dividend yield, T=Time to maturity and N denotes taking the normal cumulative probability. b = (r - q) = cost of carry. (via VinegarHill-Financelab )
Things to know
This can only be used on the daily timeframe
You must select the option type and the greeks you wish to show
This indicator is a work in process, functions may be updated in the future. I will also be adding additional greeks as I code them or they become available in finance literature. This indictor contains 18 greeks. Many more will be added later.
Inputs
Spot price: select from 33 different types of price inputs
Calculation Steps: how many iterations to be used in the BS model. In practice, this number would be anywhere from 5000 to 15000, for our purposes here, this is limited to 300
Strike Price: the strike price of the option you're wishing to model
% Implied Volatility: here you can manually enter implied volatility
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the BS process, this is to serve as a sort of benchmark for the implied volatility ,
Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these
Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country
% Manual Risk-free Rate: here you can manually enter the risk-free rate
Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate
% Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield
Adjust for Dividends?: choose if you even want to use use dividends
Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation
Time Now Type: choose how you want to calculate time right now, see the tool tip
Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc
Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours
Expiry date settings: here you can specify the exact time the option expires
The Black Scholes Greeks
The Option Greek formulae express the change in the option price with respect to a parameter change taking as fixed all the other inputs. ( Haug explores multiple parameter changes at once .) One significant use of Greek measures is to calibrate risk exposure. A market-making financial institution with a portfolio of options, for instance, would want a snap shot of its exposure to asset price, interest rates, dividend fluctuations. It would try to establish impacts of volatility and time decay. In the formulae below, the Greeks merely evaluate change to only one input at a time. In reality, we might expect a conflagration of changes in interest rates and stock prices etc. (via VigengarHill-Financelab )
First-order Greeks
Delta: Delta measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price. Delta is the first derivative of the value
Vega: Vegameasures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset.
Theta: Theta measures the sensitivity of the value of the derivative to the passage of time (see Option time value): the "time decay."
Rho: Rho measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term).
Lambda: Lambda, Omega, or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.
Epsilon: Epsilon, also known as psi, is the percentage change in option value per percentage change in the underlying dividend yield, a measure of the dividend risk. The dividend yield impact is in practice determined using a 10% increase in those yields. Obviously, this sensitivity can only be applied to derivative instruments of equity products.
Second-order Greeks
Gamma: Measures the rate of change in the delta with respect to changes in the underlying price. Gamma is the second derivative of the value function with respect to the underlying price.
Vanna: Vanna, also referred to as DvegaDspot and DdeltaDvol, is a second order derivative of the option value, once to the underlying spot price and once to volatility. It is mathematically equivalent to DdeltaDvol, the sensitivity of the option delta with respect to change in volatility; or alternatively, the partial of vega with respect to the underlying instrument's price. Vanna can be a useful sensitivity to monitor when maintaining a delta- or vega-hedged portfolio as vanna will help the trader to anticipate changes to the effectiveness of a delta-hedge as volatility changes or the effectiveness of a vega-hedge against change in the underlying spot price.
Charm: Charm or delta decay measures the instantaneous rate of change of delta over the passage of time.
Vomma: Vomma, volga, vega convexity, or DvegaDvol measures second order sensitivity to volatility. Vomma is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes.
Veta: Veta or DvegaDtime measures the rate of change in the vega with respect to the passage of time. Veta is the second derivative of the value function; once to volatility and once to time.
Vera: Vera (sometimes rhova) measures the rate of change in rho with respect to volatility. Vera is the second derivative of the value function; once to volatility and once to interest rate.
Third-order Greeks
Speed: Speed measures the rate of change in Gamma with respect to changes in the underlying price.
Zomma: Zomma measures the rate of change of gamma with respect to changes in volatility.
Color: Color, gamma decay or DgammaDtime measures the rate of change of gamma over the passage of time.
Ultima: Ultima measures the sensitivity of the option vomma with respect to change in volatility.
Dual Delta: Dual Delta determines how the option price changes in relation to the change in the option strike price; it is the first derivative of the option price relative to the option strike price
Dual Gamma: Dual Gamma determines by how much the coefficient will changedual delta when the option strike price changes; it is the second derivative of the option price relative to the option strike price.
Related Indicators
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Implied Volatility Estimator using Black Scholes
Boyle Trinomial Options Pricing Model
Black-Scholes Model and Greeks for European OptionsThe Black-Scholes model is a mathematical model used for pricing options. From this model you can derive the theoretical fair value of a European option (an option where you have to wait until expiry to exercise). Additionally, you can derive various risk parameters called Greeks. This indicator includes three types of data: Theoretical Option Price (blue), the Greeks (green), and implied volatility (red); their values are presented in that order.
1) Theoretical Option Price:
This first value gives only the theoretical fair value of an option with a given strike based on the Black-Scholes framework. Remember this is a model and does not reflect actual option prices, just the theoretical price based on the Black-Scholes model and its parameters and assumptions.
2)Greeks (all of the Greeks included in this indicator are listed below):
a)Delta is the rate of change of the theoretical option price with respect to the change in the underlying's price. This can also be used to approximate the probability of your option expiring in the money. For example, if you have an option with a delta of 0.62, then it has about a 62% chance of expiring in-the-money. This number runs from 0 to 1 for Calls, and 0 to -1 for Puts.
b)Gamma is the rate of change of delta with respect to the change in the underlying's price.
c)Theta, aka "time decay", is the rate of change in the theoretical option price with respect to the change in time. Theta tells you how much an option will lose its value day by day.
d)Vega is the rate of change in the theoretical option price with respect to change in implied volatility.
e)Rho is the rate of change in the theoretical option price with respect to change in the risk-free rate. Rho is rarely used because it is the parameter that options are least effected by, it is more useful for longer term options, like LEAPs.
f)Vanna is the sensitivity of delta to changes in implied volatility. Vanna is useful for checking the effectiveness of delta-hedged and vega-hedged portfolios.
g)Charm, aka "delta decay", is the instantaneous rate of change of delta over time. Charm is useful for monitoring delta-hedged positions.
h)Vomma measures the sensitivity of vega to changes in implied volatility.
i)Veta measures the rate of change in vega with respect to time.
j)Vera measures the rate of change of rho with respect to implied volatility.
k)Speed measures the rate of change in gamma with respect to changes in the underlying's price. Speed can be used when evaluating delta-hedged and gamma hedged portfolios.
l)Zomma measures the rate of change in gamma with respect to changes in implied volatility. Zomma can be used to evaluate the effectiveness of a gamma-hedged portfolio.
m)Color, aka "gamma decay", measures the rate of change of gamma over time. This can also be used to evaluate the effectiveness of a gamma-hedged portfolio.
n)Ultima measures the rate of change in vomma with respect to implied volatility.
o)Probability of Touch, is not a Greek, but a metric that I included, which tells you the probability of price touching your strike price before expiry.
3) Implied Volatility:
This is the market's forecast of future volatility. Implied volatility is directionless, it cannot be used to forecast future direction. All it tells you is the forecast for future volatility.
How to use this indicator:
1st. Input the strike price of your option. If you input a strike that is more than 3 standard deviations away from the current price, the model will return a value of n/a.
2nd. Input the current risk-free rate.(Including this is optional, because the risk-free rate is so small, you can just leave this number at zero.)
3rd. Input the time until expiry. You can enter this in terms of days, hours, and minutes.
4th.Input the chart time frame you are using in terms of minutes. For example if you're using the 1min time frame input 1, 4 hr time frame input 480, daily time frame input 1440, etc.
5th. Pick what type of option you want data for, Long Call or Long Put.
6th. Finally, pick which Greek you want displayed from the drop-down list.
*Remember the Option price presented, and the Greeks presented, are theoretical in nature, and not based upon actual option prices. Also, remember the Black-Scholes model is just a model based upon various parameters, it is not an actual representation of reality, only a theoretical one.
VolbandsThe Volbands indicator dynamically plots upper and lower volatility bands based on implied daily moves derived from volatility indices. This tool provides a visual forecast of the next trading day's price range, helping traders anticipate potential price movement boundaries.
Key Features:
1. Auto-Detect Volatility Index: Volbands automatically detects the appropriate volatility index based on the current symbol. For example, it uses the VIX for S&P 500, VXN for Nasdaq 100, and custom indexes like VXAPL for Apple. Users can also manually select a specific volatility index if preferred.
2. Projected Bands:
- The indicator plots the projected upper and lower bands for the next trading day using the implied move from the volatility index.
- Displays today’s projected bands as a reference and overlays next day’s bands with a slight offset, visually indicating the anticipated range.
3. Dynamic Updates: The indicator updates automatically as new bars are added, ensuring that users have up-to-date projections based on the latest volatility data.
4. Highlighting Extreme Price Action: Candles that close outside of the projected bands are colored in yellow, highlighting moments of higher-than-expected volatility.
5. Informative Table: A customizable table displays relevant information, including:
- The selected or auto-detected volatility index
- Implied daily move percentage
- Projected upper and lower levels
Potential Applications:
- Risk Management: The Volbands indicator can help traders set more informed stop-loss and take-profit levels based on volatility-driven price projections.
- Identifying Overbought/Oversold Conditions: Price movement outside the projected bands may indicate overbought or oversold conditions, potentially signaling trade opportunities.
-Enhancing Entry and Exit Points: The projected bands act as soft support and resistance levels, assisting traders in timing entries and exits in anticipation of volatility-driven price reactions.
Future Enhancements:
Potential improvements to expand functionality could include:
- Additional Volatility Indices: Expanding coverage to include more assets and volatility indices.
- Alerts: Setting alerts for when prices breach the projected bands, enabling traders to react quickly to unexpected price movements.
- Customization of Bands: Adding options for users to adjust the implied move percentage, creating customized bands that reflect individual trading strategies.
This indicator combines implied volatility with price action, offering valuable insights to traders on expected price ranges and volatility.
VIX AnalyticsThis script is designed to serve traders, analysts, and investors who want a real-time, comprehensive view of market volatility, risk sentiment, and implied movements. It combines multiple institutional-grade volatility indices into one clear dashboard and interprets them with actionable insights — directly on your chart.
🔍 Features Included
🟦VIX (CBOE Volatility Index)
Measures market expectation of 30-day S&P 500 volatility.
Color-coded interpretation ranges:
Under 13: Extreme Complacency
15–20: Stable Market
20–30: Moderate Risk
30–40: High Volatility
Over 40: Panic
🟪 VVIX (Volatility of Volatility Index)
Tracks the volatility of VIX itself.
Interpreted as a risk gauge of how aggressively traders are hedging volatility exposure.
Under 80: Market Complacency
80–100: Normal Environment
100–120: Caution — Rising Volatility of Volatility
Over 120: High Stress — Elevated Hedging Activity
🟨 SKEW Index
Measures the perceived tail risk of the S&P 500 — i.e., the probability of a black swan event.
Below 110: Potential Complacency
120–140: Moderate Tail Risk
Above 140: High Tail Risk
🧮 VIX/VVIX Ratio
Gauges relative fear levels between expected volatility and the volatility of volatility.
Under 0.5: Low Ratio — VVIX Overextended
Over 0.9: High Ratio — VIX Leading
📈 VIX Percentile (1-Year Range)
Shows where the current VIX sits relative to its 1-year high/low.
Under 20%: Volatility is Cheap
Over 70%: Fear is Elevated — Reversal Possible
📉 SPX Implied Point Moves
Projects expected moves in SPX using VIX-derived volatility:
Daily
Weekly
Monthly
Helps size positions or define expected price ranges based on volatility regime.
📊 ATR Values (5, 13, 21 periods)
Traditional volatility using historical prices.
Provided alongside implied data for comparison.
🧠 Unique Logic & Interpretation Layer
This script doesn’t just show raw data — it interprets it. It reads the relationship between VIX, VVIX, and SKEW to highlight:
When market volatility may be underpriced
When hidden tail risks are forming
When to be cautious of volatility expansions
How current implied movement compares to past realized volatility
✅ Use Cases
Day traders: Know when volatility is low or expanding before scalping or swinging.
Options traders: Identify whether implied volatility is cheap or expensive.
Portfolio managers: Gauge when hedging is in demand and adjust exposure.
Risk managers: Crosscheck if current volatility aligns with macro risk events.
⚙️ Settings
Customizable table placement: Move the dashboard to any corner of your chart.
No repainting or lag: Data updates in real-time using official CBOE and SPX feeds.
Black-Scholes Options Pricing ModelThis is an updated version of my "Black-Scholes Model and Greeks for European Options" indicator, that i previously published. I decided to make this updated version open-source, so people can tweak and improve it.
The Black-Scholes model is a mathematical model used for pricing options. From this model you can derive the theoretical fair value of an options contract. Additionally, you can derive various risk parameters called Greeks. This indicator includes three types of data: Theoretical Option Price (blue), the Greeks (green), and implied volatility (red); their values are presented in that order.
1) Theoretical Option Price:
This first value gives only the theoretical fair value of an option with a given strike based on the Black-Scholes framework. Remember this is a model and does not reflect actual option prices, just the theoretical price based on the Black-Scholes model and its parameters and assumptions.
2)Greeks (all of the Greeks included in this indicator are listed below):
a)Delta is the rate of change of the theoretical option price with respect to the change in the underlying's price. This can also be used to approximate the probability of your option expiring in the money. For example, if you have an option with a delta of 0.62, then it has about a 62% chance of expiring in-the-money. This number runs from 0 to 1 for Calls, and 0 to -1 for Puts.
b)Gamma is the rate of change of delta with respect to the change in the underlying's price.
c)Theta, aka "time decay", is the rate of change in the theoretical option price with respect to the change in time. Theta tells you how much an option will lose its value day by day.
d) Vega is the rate of change in the theoretical option price with respect to change in implied volatility .
e)Rho is the rate of change in the theoretical option price with respect to change in the risk-free rate. Rho is rarely used because it is the parameter that options are least effected by, it is more useful for longer term options, like LEAPs.
f)Vanna is the sensitivity of delta to changes in implied volatility . Vanna is useful for checking the effectiveness of delta-hedged and vega-hedged portfolios.
g)Charm, aka "delta decay", is the instantaneous rate of change of delta over time. Charm is useful for monitoring delta-hedged positions.
h)Vomma measures the sensitivity of vega to changes in implied volatility .
i)Veta measures the rate of change in vega with respect to time.
j)Vera measures the rate of change of rho with respect to implied volatility .
k)Speed measures the rate of change in gamma with respect to changes in the underlying's price. Speed can be used when evaluating delta-hedged and gamma hedged portfolios.
l)Zomma measures the rate of change in gamma with respect to changes in implied volatility . Zomma can be used to evaluate the effectiveness of a gamma-hedged portfolio.
m)Color, aka "gamma decay", measures the rate of change of gamma over time. This can also be used to evaluate the effectiveness of a gamma-hedged portfolio.
n)Ultima measures the rate of change in vomma with respect to implied volatility .
o)Probability of Touch, is not a Greek, but a metric that I included, which tells you the probability of price touching your strike price before expiry.
3) Implied Volatility:
This is the market's forecast of future volatility . Implied volatility is directionless, it cannot be used to forecast future direction. All it tells you is the forecast for future volatility.
How to use this indicator:
1st. Input the strike price of your option. If you input a strike that is more than 3 standard deviations away from the current price, the model will return a value of n/a.
2nd. Input the current risk-free rate.(Including this is optional, because the risk-free rate is so small, you can just leave this number at zero.)
3rd. Input the time until expiry. You can enter this in terms of days, hours, and minutes.
4th.Input the chart time frame you are using in terms of minutes. For example if you're using the 1min time frame input 1, 4 hr time frame input 480, daily time frame input 1440, etc.
5th. Pick what style of option you want data for, European Vanilla or Binary.
6th. Pick what type of option you want data for, Long Call or Long Put.
7th . Finally, pick which Greek you want displayed from the drop-down list.
*Remember the Option price presented, and the Greeks presented, are theoretical in nature, and not based upon actual option prices. Also, remember the Black-Scholes model is just a model based upon various parameters, it is not an actual representation of reality, only a theoretical one.
*Note 1. If you choose binary, only data for Long Binary Calls will be presented. All of the Greeks for Long Binary Calls are available, except for rho and vera because they are negligible.
*Note 2. Unlike vanilla european options, the delta of a binary option cannot be used to approximate the probability of the option expiring in-the-money. For binary options, if you want to approximate the probability of the binary option expiring in-the-money, use the price. The price of a binary option can be used to approximate its probability of expiring in-the-money. So if a binary option has a price of $40, then it has approximately a 40% chance of expiring in-the-money.
*Note 3. As time goes on you will have to update the expiry, this model does not do that automatically. So for example, if you originally have an option with 30 days to expiry, tomorrow you would have to manually update that to 29 days, then the next day manually update the expiry to 28, and so on and so forth.
There are various formulas that you can use to calculate the Greeks. I specifically chose the formulations included in this indicator because the Greeks that it presents are the closest to actual options data. I compared the Greeks given by this indicator to brokerage option data on a variety of asset classes from equity index future options to FX options and more. Because the indicator does not use actual option prices, its Greeks do not match the brokerage data exactly, but are close enough.
I may try to make future updates that include data for Long Binary Puts, American Options, Asian Options, etc.
VIX Statistical Sentiment Index [Nasan]** THIS IS ONLY FOR US STOCK MARKET**
The indicator analyzes market sentiment by computing the Rate of Change (ROC) for the VIX and S&P 500, visualizing the data as histograms with conditional coloring. It measures the correlation between the VIX, the specific stock, and the S&P 500, displaying the results on the chart. The reliability measure combines these correlations, offering an overall assessment of data robustness. One can use this information to gauge the inverse relationship between VIX and S&P 500, the alignment of the specific stock with the market, and the overall reliability of the correlations for informed decision-making based on the inverse relationship of VIX and price movement.
**WHEN THE VIX ROC IS ABOVE ZERO (RED COLOR) AND RASING ONE CAN EXPECT THE PRICE TO MOVE DOWNWARDS, WHEN THE VIX ROC IS BELOW ZERO (GREEN)AND DECREASING ONE CAN EXPECT THE PRICE TO MOVE UPWARDS"
Understanding the VIX Concept:
The VIX, or Volatility Index, is a widely used indicator in finance that measures the market's expectation of volatility over the next 30 days. Here are key points about the VIX:
Fear Gauge:
Often referred to as the "fear gauge," the VIX tends to rise during periods of market uncertainty or fear and fall during calmer market conditions.
Inverse Relationship with Market:
The VIX typically has an inverse relationship with the stock market. When the stock market experiences a sell-off, the VIX tends to rise, indicating increased expected volatility.
Implied Volatility:
The VIX is derived from the prices of options on the S&P 500. It represents the market's expectations for future volatility and is often referred to as "implied volatility."
Contrarian Indicator:
Extremely high VIX levels may indicate oversold conditions, suggesting a potential market rebound. Conversely, very low VIX levels may signal complacency and a potential reversal.
VIX vs. SPX Correlation:
This correlation measures the strength and direction of the relationship between the VIX (Volatility Index) and the S&P 500 (SPX).
A negative correlation indicates an inverse relationship. When the VIX goes up, the SPX tends to go down, and vice versa.
The correlation value closer to -1 suggests a stronger inverse relationship between VIX and SPX.
Stock vs. SPX Correlation:
This correlation measures the strength and direction of the relationship between the closing price of the stock (retrieved using src1) and the S&P 500 (SPX).
This correlation helps assess how closely the stock's price movements align with the broader market represented by the S&P 500.
A positive correlation suggests that the stock tends to move in the same direction as the S&P 500, while a negative correlation indicates an opposite movement.
Reliability Measure:
Combines the squared values of the VIX vs. SPX and Stock vs. SPX correlations and takes the square root to create a reliability measure.
This measure provides an overall assessment of how reliable the correlation information is in guiding decision-making.
Interpretation:
A higher reliability measure implies that the correlations between VIX and SPX, as well as between the stock and SPX, are more robust and consistent.
One can use this reliability measure to gauge the confidence they can place in the correlations when making decisions about the specific stock based on VIX data and its correlation with the broader market.
L&S Volatility Index Refurbished█ Introduction
This is my second version of the L&S Volatility Index, hence the name "Refurbished".
The first version can be found at this link:
The reason I released a separate version is because I rewrote the source code from scratch with the aim of both improving the indicator and staying as close as possible to the original concept.
I feel that the first version was somewhat exotic and polluted in relation to the indicator originally described by the authors.
In short, the main idea remains the same, however, the way of presenting the result has been changed, reiterating what was said.
█ CONCEPTS
The L&S Volatility Index measures the volatility of price in relation to a moving average.
The indicator was originally described by Brazilian traders Alexandre Wolwacz (Stormer) and Fábio Figueiredo (Vlad) from L&S Educação Financeira.
Basically, this indicator can be used in two ways:
1. In a mean reversion strategy, when there is an unusual distance from it;
2. In a trend following strategy, when the price is in an acceptable region.
As an indicator of volatility, the greatest utility is shown in first case.
This is because it allows identifying abnormal prices, extremely stretched in relation to an average, including market crashes.
How the calculation is done:
First, the distance of the price from a given average in percentage terms is measured.
Then, the historical average volatility is obtained.
Finally the indicator is calculated through the ratio between the distance and the historical volatility.
According to the description proposed by the creators, when the L&S Volatility Index is above 30 it means that the price is "stretched".
The closer to 100 the more stretched.
When it reaches 0, it means the price is on average.
█ What to look for
Basically, you should look at non-standard prices.
How to identify it?
When the oscillator is outside the Dynamic Zone and/or the Fixed Zone (above 30), it is because the price is stretched.
Nothing on the market is guaranteed.
As with the RSI, it is not because the RSI is overbought or oversold that the price will necessarily go down or up.
It is critical to know when NOT to buy, NOT to sell or NOT to do anything.
It is always important to consider the context.
█ Improvements
The following improvements have been implemented.
It should be noted that these improvements can be disabled, thus using the indicator in the "purest" version, the same as the one conceived by the creators.
Resources:
1. Customization of limits and zones:
2. Customization of the timeframe, which can be different from the current one.
3. Repaint option (prints the indicator in real time even if the bar has not yet closed. This produces more signals).
4. Customization of price inputs. This affects the calculation.
5. Customization of the reference moving average (the moving average used to calculate the price distance).
6. Customization of the historical volatility calculation strategy.
- Accumulated ATR: calculates the historical volatility based on the accumulated ATR.
- Returns: calculates the historical volatility based on the returns of the source.
Both forms of volatility calculation have their specific utilities and applications.
Therefore, it is worthwhile to have both approaches available, and one should not necessarily replace the other.
Each method has its advantages and may be more appropriate in different contexts.
The first approach, using the accumulated ATR, can be useful when you want to take into account the implied volatility of prices over time,
reflecting broader price movements and higher impact events. It can be especially relevant in scenarios where unexpected events can drastically affect prices.
The second approach, using the standard deviation of returns, is more common and traditionally used to measure historical volatility.
It considers the variability of prices relative to their average, providing a more general measure of market volatility.
Therefore, both forms of calculation have their merits and can be useful depending on the context and specific analysis needs.
Having both options available gives users flexibility in choosing the most appropriate volatility measure for the situation at hand.
* When choosing "Accumulated ATR", if the indicator becomes difficult to see, there are 3 possibilities:
a) manually adjust the Fixed Zone value;
b) disable the Fixed Zone and use only the Dynamic Zone;
c) normalize the indicator.
7. Signal line (a moving average of the oscillator).
8. Option to normalize the indicator or not.
9. Colors to facilitate direction interpretation.
Since the L&S is a volatility indicator, it does not show whether the price is rising or falling.
This can sometimes confuse the user.
That said, the idea here is to show certain colors where the price is relative to the average, making it easier to analyze.
10. Alert messages for automations.
vol_rangesThis script shows three measures of volatility:
historical (hv): realized volatility of the recent past
median (mv): a long run average of realized volatility
implied (iv): a user-defined volatility
Historical and median volatility are based on the EWMA, rather than standard deviation, method of calculating volatility. Since Tradingview's built in ema function uses a window, the "window" parameter determines how much historical data is used to calculate these volatility measures. E.g. 30 on a daily chart means the previous 30 days.
The plots above and below historical candles show past projections based on these measures. The "periods to expiration" dictates how far the projection extends. At 30 periods to expiration (default), the plot will indicate the one standard deviation range from 30 periods ago. This is calculated by multiplying the volatility measure by the square root of time. For example, if the historical volatility (hv) was 20% and the window is 30, then the plot is drawn over: close * 1.2 * sqrt(30/252).
At the most recent candle, this same calculation is simply drawn as a line projecting into the future.
This script is intended to be used with a particular options contract in mind. For example, if the option expires in 15 days and has an implied volatility of 25%, choose 15 for the window and 25 for the implied volatility options. The ranges drawn will reflect the two standard deviation range both in the future (lines) and at any point in the past (plots) for HV (blue), MV (red), and IV (grey).
Implied and Historical VolatilityAbstract
This TradingView indicator visualizes implied volatility (IV) derived from the VIX index and historical volatility (HV) computed from past price data of the S&P 500 (or any selected asset). It enables users to compare market participants' forward-looking volatility expectations (via VIX) with realized past volatility (via historical returns). Such comparisons are pivotal in identifying risk sentiment, volatility regimes, and potential mispricing in derivatives.
Functionality
Implied Volatility (IV):
The implied volatility is extracted from the VIX index, often referred to as the "fear gauge." The VIX represents the market's expectation of 30-day forward volatility, derived from options pricing on the S&P 500. Higher values of VIX indicate increased uncertainty and risk aversion (Whaley, 2000).
Historical Volatility (HV):
The historical volatility is calculated using the standard deviation of logarithmic returns over a user-defined period (default: 20 trading days). The result is annualized using a scaling factor (default: 252 trading days). Historical volatility represents the asset's past price fluctuation intensity, often used as a benchmark for realized risk (Hull, 2018).
Dynamic Background Visualization:
A dynamic background is used to highlight the relationship between IV and HV:
Yellow background: Implied volatility exceeds historical volatility, signaling elevated market expectations relative to past realized risk.
Blue background: Historical volatility exceeds implied volatility, suggesting the market might be underestimating future uncertainty.
Use Cases
Options Pricing and Trading:
The disparity between IV and HV provides insights into whether options are over- or underpriced. For example, when IV is significantly higher than HV, options traders might consider selling volatility-based derivatives to capitalize on elevated premiums (Natenberg, 1994).
Market Sentiment Analysis:
Implied volatility is often used as a proxy for market sentiment. Comparing IV to HV can help identify whether the market is overly optimistic or pessimistic about future risks.
Risk Management:
Institutional and retail investors alike use volatility measures to adjust portfolio risk exposure. Periods of high implied or historical volatility might necessitate rebalancing strategies to mitigate potential drawdowns (Campbell et al., 2001).
Volatility Trading Strategies:
Traders employing volatility arbitrage can benefit from understanding the IV/HV relationship. Strategies such as "long gamma" positions (buying options when IV < HV) or "short gamma" (selling options when IV > HV) are directly informed by these metrics.
Scientific Basis
The indicator leverages established financial principles:
Implied Volatility: Derived from the Black-Scholes-Merton model, implied volatility reflects the market's aggregate expectation of future price fluctuations (Black & Scholes, 1973).
Historical Volatility: Computed as the realized standard deviation of asset returns, historical volatility measures the intensity of past price movements, forming the basis for risk quantification (Jorion, 2007).
Behavioral Implications: IV often deviates from HV due to behavioral biases such as risk aversion and herding, creating opportunities for arbitrage (Baker & Wurgler, 2007).
Practical Considerations
Input Flexibility: Users can modify the length of the HV calculation and the annualization factor to suit specific markets or instruments.
Market Selection: The default ticker for implied volatility is the VIX (CBOE:VIX), but other volatility indices can be substituted for assets outside the S&P 500.
Data Frequency: This indicator is most effective on daily charts, as VIX data typically updates at a daily frequency.
Limitations
Implied volatility reflects the market's consensus but does not guarantee future accuracy, as it is subject to rapid adjustments based on news or events.
Historical volatility assumes a stationary distribution of returns, which might not hold during structural breaks or crises (Engle, 1982).
References
Black, F., & Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81(3), 637-654.
Whaley, R. E. (2000). "The Investor Fear Gauge." The Journal of Portfolio Management, 26(3), 12-17.
Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson Education.
Natenberg, S. (1994). Option Volatility and Pricing: Advanced Trading Strategies and Techniques. McGraw-Hill.
Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (2001). The Econometrics of Financial Markets. Princeton University Press.
Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill.
Baker, M., & Wurgler, J. (2007). "Investor Sentiment in the Stock Market." Journal of Economic Perspectives, 21(2), 129-151.
Williams Vix Fix ultra complete indicator (Tartigradia)Williams VixFix is a realized volatility indicator developed by Larry Williams, and can help in finding market bottoms.
Indeed, as Williams describe in his paper, markets tend to find the lowest prices during times of highest volatility, which usually accompany times of highest fear. The VixFix is calculated as how much the current low price statistically deviates from the maximum within a given look-back period.
Although the VixFix originally only indicates market bottoms, its inverse may indicate market tops. As masa_crypto writes : "The inverse can be formulated by considering "how much the current high value statistically deviates from the minimum within a given look-back period." This transformation equates Vix_Fix_inverse. This indicator can be used for finding market tops, and therefore, is a good signal for a timing for taking a short position." However, in practice, the Inverse VixFix is much less reliable than the classical VixFix, but is nevertheless a good addition to get some additional context.
For more information on the Vix Fix, which is a strategy published under public domain:
* The VIX Fix, Larry Williams, Active Trader magazine, December 2007, web.archive.org
* Fixing the VIX: An Indicator to Beat Fear, Amber Hestla-Barnhart, Journal of Technical Analysis, March 13, 2015, ssrn.com
* Replicating the CBOE VIX using a synthetic volatility index trading algorithm, Dayne Cary and Gary van Vuuren, Cogent Economics & Finance, Volume 7, 2019, Issue 1, doi.org
Created By ChrisMoody on 12-26-2014...
V3 MAJOR Update on 1-05-2014
tista merged LazyBear's Black Dots filter in 2020:
Extended by Tartigradia in 10-2022:
* Can select a symbol different from current to calculate vixfix, allows to select SP:SPX to mimic the original VIX index.
* Inverse VixFix (from masa_crypto and web.archive.org)
* VixFix OHLC Bars plot
* Price / VixFix Candles plot (Pro Tip: draw trend lines to find good entry/exit points)
* Add ADX filtering, Minimaxis signals, Minimaxis filtering (from samgozman )
* Convert to pinescript v5
* Allow timeframe selection (MTF)
* Skip off days (more accurate reproduction of original VIX)
* Reorganized, cleaned up code, commented out parts, commented out or removed unused code (eg, some of the KC calculations)
* Changed default Bollinger Band settings to reduce false positives in crypto markets.
Set Index symbol to SPX, and index_current = false, and timeframe Weekly, to reproduce the original VIX as close as possible by the VIXFIX (use the Add Symbol option, because you want to plot CBOE:VIX on the same timeframe as the current chart, which may include extended session / weekends). With the Weekly timeframe, off days / extended session days should not change much, but with lower timeframes this is important, because nights and weekends can change how the graph appears and seemingly make them different because of timing misalignment when in reality they are not when properly aligned.
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks [Loxx]Black-Scholes 1973 OPM on Non-Dividend Paying Stocks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. Making b equal to r yields the BSM model where dividends are not considered. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. For our purposes here are, Analytical Greeks are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
**This version of the Black-Scholes formula can also be used to price American call options on a non-dividend-paying stock, since it will never be optimal to exercise the option before expiration.**
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Generalized Black-Scholes-Merton w/ Analytical Greeks [Loxx]Generalized Black-Scholes-Merton w/ Analytical Greeks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton (BSM) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega, DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Asay (1982) Margined Futures Option Pricing Model [Loxx]Asay (1982) Margined Futures Option Pricing Model is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures where premium is fully margined. This means the Risk-free Rate, dividend, and cost to carry are all zero. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model.
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model. <== this is the one used for this indicator!
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Black-76 Options on Futures [Loxx]Black-76 Options on Futures is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho futures option
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model. <== this is the one used for this indicator!
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model.
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Garman and Kohlhagen (1983) for Currency Options [Loxx]Garman and Kohlhagen (1983) for Currency Options is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version of BSMOPM is to price Currency Options. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP, Speed
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing for Currency Options
The Garman and Kohlhagen (1983) modified Black-Scholes model can be used to price European currency options; see also Grabbe (1983). The model is mathematically equivalent to the Merton (1973) model presented earlier. The only difference is that the dividend yield is replaced by the risk-free rate of the foreign currency rf:
c = S * e^(-rf * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^(-rf * T) * N(-d1)
where
d1 = (log(S / X) + (r - rf + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
For more information on currency options, see DeRosa (2000)
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
rf = Risk-free rate of the foreign currency
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Related indicators:
BSM OPM 1973 w/ Continuous Dividend Yield
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks
Generalized Black-Scholes-Merton w/ Analytical Greeks
Generalized Black-Scholes-Merton Option Pricing Formula
Sprenkle 1964 Option Pricing Model w/ Num. Greeks
Modified Bachelier Option Pricing Model w/ Num. Greeks
Bachelier 1900 Option Pricing Model w/ Numerical Greeks
