Candle Counter [theEccentricTrader]█ OVERVIEW
This indicator counts the number of confirmed candle scenarios on any given candlestick chart and displays the statistics in a table, which can be repositioned and resized at the user's discretion.
█ CONCEPTS
Green and Red Candles
A green candle is one that closes with a high price equal to or above the price it opened.
A red candle is one that closes with a low price that is lower than the price it opened.
Upper Candle Trends
A higher high candle is one that closes with a higher high price than the high price of the preceding candle.
A lower high candle is one that closes with a lower high price than the high price of the preceding candle.
A double-top candle is one that closes with a high price that is equal to the high price of the preceding candle.
Lower Candle Trends
A higher low candle is one that closes with a higher low price than the low price of the preceding candle.
A lower low candle is one that closes with a lower low price than the low price of the preceding candle.
A double-bottom candle is one that closes with a low price that is equal to the low price of the preceding candle.
█ FEATURES
Inputs
Start Date
End Date
Position
Text Size
Show Sample Period
Show Plots
Table
The table is colour coded, consists of three columns and twenty-two rows. Blue cells denote all candle scenarios, green cells denote green candle scenarios and red cells denote red candle scenarios.
The candle scenarios are listed in the first column with their corresponding total counts to the right, in the second column. The last row in column one, row twenty-two, displays the sample period which can be adjusted or hidden via indicator settings.
Rows two and three in the third column of the table display the total green and red candles as percentages of total candles. Rows four to nine in column three, coloured blue, display the corresponding candle scenarios as percentages of total candles. Rows ten to fifteen in column three, coloured green, display the corresponding candle scenarios as percentages of total green candles. And lastly, rows sixteen to twenty-one in column three, coloured red, display the corresponding candle scenarios as percentages of total red candles.
Plots
I have added plots as a visual aid to the various candle scenarios listed in the table. Green up-arrows denote higher high candles when above bar and higher low candles when below bar. Red down-arrows denote lower high candles when above bar and lower low candles when below bar. Similarly, blue diamonds when above bar denote double-top candles and when below bar denote double-bottom candles. These plots can also be hidden via indicator settings.
█ HOW TO USE
This indicator is intended for research purposes and strategy development. I hope it will be useful in helping to gain a better understanding of the underlying dynamics at play on any given market and timeframe. It can, for example, give you an idea of any inherent biases such as a greater proportion of green candles to red. Or a greater proportion of higher low green candles to lower low green candles. Such information can be very useful when conducting top down analysis across multiple timeframes, or considering trailing stop loss methods.
What you do with these statistics and how far you decide to take your research is entirely up to you, the possibilities are endless.
This is just the first and most basic in a series of indicators that can be used to study objective price action scenarios and develop a systematic approach to trading.
█ LIMITATIONS
Some higher timeframe candles on tickers with larger lookbacks such as the DXY, do not actually contain all the open, high, low and close (OHLC) data at the beginning of the chart. Instead, they use the close price for open, high and low prices. So, while we can determine whether the close price is higher or lower than the preceding close price, there is no way of knowing what actually happened intra-bar for these candles. And by default candles that close at the same price as the open price, will be counted as green. You can avoid this problem by utilising the sample period filter.
The green and red candle calculations are based solely on differences between open and close prices, as such I have made no attempt to account for green candles that gap lower and close below the close price of the preceding candle, or red candles that gap higher and close above the close price of the preceding candle. I can only recommend using 24-hour markets, if and where possible, as there are far fewer gaps and, generally, more data to work with. Alternatively, you can replace the scenarios with your own logic to account for the gap anomalies, if you are feeling up to the challenge.
It is also worth noting that the sample size will be limited to your Trading View subscription plan. Premium users get 20,000 candles worth of data, pro+ and pro users get 10,000, and basic users get 5,000. If upgrading is currently not an option, you can always keep a rolling tally of the statistics in an excel spreadsheet or something of the like.
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+ Average Candle Bodies RangeACBR, or, Average Candle Bodies Range is a volatility and momentum indicator designed to indicate periods of increasing volatility and/or momentum. The genesis of the idea formed from my pondering what a trend trader is really looking for in terms of a volatility indicator. Most indicators I've come across haven't, in my opinion, done a satisfactory job of highlighting this. I kept thinking about the ATR (I use it for stops and targets) but I realized I didn't care about highs or lows in regards to a candle's volatility or momentum, nor do I care about their relation to a previous close. What really matters to me is candle body expansion. That is all. So, I created this.
ACBR is extremely simple at its heart. I made it more complicated of course, because why would I want anything for myself to be simple? Originally it was envisaged to be a simple volatility indicator highlighting areas of increasing and decreasing volatility. Then I decided some folks might want an indicator that could show this in a directional manner, i.e., an oscillator, so I spent some more hours tackling that
To start, the original version of the indicator simply subtracts opening price from closing price if the candle closes above the open, and subtracts the close from the open if the candle closes below the open. This way we get a positive number that simply measures candle expansion. We then apply a moving average to these values in order to smooth them (if you want). To get an oscillator we always subtract the close from the open, thus when a candle closes below its open we get a negative number.
I've naturally added an optional signal line as a helpful way of gauging volatility because obviously the values themselves may not tell you much. But I've also added something that I call a baseline. You can use this in a few ways, but first let me explain the two options for how the baseline can be calculated. And what do I mean by 'baseline?' I think of it as an area of the indicator where if the ACBR is below you will not want to enter into any trades, and if the ACBR is above then you are free to enter trades based on your system (or you might want to enter in areas of low volatility if your system calls for that). Waddah Attar Explosion is another indicator that implements something similar. The baseline is calculated in two different ways: one of which is making a Donchian Channel of the ACBR, and then using the basis as the baseline, while the other is applying an RMA to the cb_dif, which is the base unit that makes up the ACBR. Now, the basis of a Donchian Channel typically is the average of the highs and the lows. If we did that here we would have a baseline much too high (but maybe not...), however, I've made the divisor user adjustable. In this way you can adjust the height (or I guess you might say 'width' if it's an oscillator) however you like, thus making the indicator more or less sensitive. In the case of using the ACBR as the baseline we apply a multiplier to the values in order to adjust the height. Apologies if I'm being overly verbose. If you want to skip all of this I have tooltips in the settings for all of the inputs that I think need an explanation.
When using the indicator as an oscillator there are baselines above and below the zero line. One funny thing: if using the ACBR as calculation type for the baselines in oscillator mode, the baselines themselves will oscillate around the zero line. There is no way to fix this due to the calculation. That isn't necessarily bad (based on my eyeball test), but I probably wouldn't use it in such a way. But experiment! They could actually be a very fine entry or confirmation indicator. And while I'm on the topic of confirmation indicators, using this indicator as an oscillator naturally makes it a confirmation indicator. It just happens to have a volatility measurement baked into it. It may also be used as an exit and continuation indicator. And speaking of these things, there are optional shapes for indicating when you might want to exit or take a continuation trade. I've added alerts for these things too.
Lastly, oscillator mode is good for identifying divergences.
Above we have the indicator set to directional, or oscillator, mode. Baselines are Donchian Channels. I changed the default EMA length from 4 to 24 in this case, otherwise all the settings are default, as in the main image for the indicator (which is clearly set to non-directional). The indicator is set to requiring an advancing signal line for background and bar colors. Background color is not on by default. Candle colors, as you can see are aqua when above the top baseline (and only when the signal line is advancing, as per the settings), magenta when below the bottom baseline, and grey for anything else. The red and blue X's are exit signals. There are two types: one, when the signal line weakens and, two, when the ACBR crosses above or below the signal line. There are also arrows. These are continuation signals (ACBR crossing signal line).
Same image as above, but the baselines are set to ACBR rather than Donchian Channels.
Again, the same image, but with everything but the ACBR Baseline turned off. You can see how this might make for an excellent confirmation indicator, but for the areas of chap. Maybe run a second instance of the indicator on your chart as a volatility indicator, as you would not be using it in that way in this instance.
Here I have bar coloring turned off except for signal line crosses NOT requiring the signal line to be advancing. Background coloring is also turned on. You can see that these all line up with continuation signals, or exits for purple candles.
Same image as above but requiring the signal line to be advancing. You can see that continuation signals are not contingent upon the signal line to be advancing. I had it setup that way at first, but of course it still gave false signals, so I thought more signals (not that there are many) is better than fewer. To be sure, just because the indicator shows a continuation signal does not mean you should always take it.
Price Legs: Time & Distance. Measuring moves in time & price-Tool to measure price legs in terms of both time and price; gives an idea of frequency of market movements and their typical extent and duration.
-Written for backtesting: seeing times of day where setups are most likely to unfold dynamically; getting an idea of typical and minimum sizes of small/large legs.
-Two sets of editable lookback numbers to measure both small and large legs independently.
-Works across timeframes and assets (units = mins/hours/days dependent on timeframe; units = '$' for indices & futures, 'pips' for FX).
~toggle on/off each set of bull/bear boxes.
~choose lookback/forward length for each set. Increase number for larger legs, decrease for smaller legs.
(for assets outside of the big Indices and FX, you may want to edit the multiplier, pMult, on lines 23-24)
small legs
large legs
Trail Blaze - (Multi Function Trailing Stop Loss) - [mutantdog]Shorter version:
As the title states, this is a 'Trailing Stop' type indicator, albeit one with a whole bunch of additional functionality, making it far more versatile and customisable than a standard trailing stop.
The main set of features includes:
Three independent trailing types each with their own +/- multipliers:
- Standard % change
- ATR (aka Supertrend)
- IQR (inter-quartile range)
These can be used in isolation or summed together. A subsequent pair of direction specific multipliers are also included.
Two separate custom source inputs are available, both feature the standard options alongside a selection of 'weighted inputs' and the option to use another indicator (selected via 'AUX'):
- 'Centre' determines the value about which the trailing sum will be added to define the stop level.
- 'Trigger' determines the value used for crossing of stops, initiating trend changes and triggering alerts.
A selection of optional filters and moving averages are available for both.
Furthermore there are various useful visualisation options available, including the underlying bands that govern the stop levels. Preset alerts for trend reversals are also included.
This is not really an 'out-of-the-box' indicator. Depending upon the market and timeframe some adjustments will be necessary for it to function in a useful manner, these can be as simple or complex as the feature-set allows. Basic settings are easy to dial in however and the default state is intended as a good starting point. Alternatively with some experimentation, a plethora of unique and creative configurations are possible, making this a great tool for tweaking. Below is a more detailed overview followed by a bunch of simple example settings.
------------------------
Lengthy Version :
DESIGN & CONCEPT
Before we start breaking this down, a little background. This started off as an attempt to improve upon the ever-popular Supertrend indicator. Of course there are many excellent user created variants available utilising some interesting methods to overcome the drawbacks of the basic version. To that end, rather than copying the work of others, the direction here shifted towards a hybrid trailing stop loss with a bunch of additional user customisation options. At some point, a completely different project involving IQR got morphed into this one. After sitting through months of sideways chop (where this proved to be of limited use), at the time of publication the market has began to form some near term trend direction and it appears to be performing well in many different timeframes.
And so with that out of the way...
INPUTS
The standard Supertrend (and most other variants) includes a single source input, as default set to 'hl2' (candle mid-range). This is the centre around which the atr bands are added/subtracted to govern the stop levels. This is not however the value which is used to trigger the trend reversal, that is usually hard-coded to 'close'. For this version both source values are adjustable: labelled 'centre' and 'trigger' respectively.
Each has custom input selectors including the usual options, a selection of 'weighted inputs' and the option to use another indicator (selected from the Aux input). The 'weighted inputs' are those introduced in Weight Gain 4000, for more details please refer to that listing. These should be treated as experimental, however may prove useful in certain configurations. In this case 'hl-oc2' can be considered an estimate of the candle median and may be a good alternative to the default 'centre' setting of 'hl2', in contrast 'cc-ohlc4' can tend to favour the extremes in the trend direction so could be useful as a faster 'trigger' than the default 'close'.
To cap them off both come with a selection of moving average filters (SMA, EMA, WMA, RMA, HMA, VWMA and a simple VWEMA - note: not elastic) aswell as median and mid-range. 'Centre' can also be set to the output of 'trigger' post-filter which can be useful if working with fast/slow crosses as the basis.
DYNAMICS
This is the main section, comprised of three separate factors: 'TSL', 'ATR' and 'IQR'. The first two should be fairly obvious, 'TSL' (trailing stop loss) is simply a percentage of the 'centre' value while 'ATR' (average true range) is the standard RMA-based version as used in Supertrend, Volatility Stop etc.
The third factor is less common however: 'IQR' (inter-quartile range). In case you are unfamiliar the principle here is, for a given dataset, the greatest 25% and smallest 25% of samples are removed. The remainder is then treated as a set and the range is calculated by highest - lowest. This is a commonly used method in statistical analysis, by removing the extremes it is less prone to influence by outliers and gives a good representation of the main dispersion around the median. In practise i have found it can be a good alternative to ATR, translating better across multiple time-frames due to it representing a fraction of the total range rather than an average of per-candle range like ATR. Used in combination with the others it can also add a factor more representative of longer-term/higher-timeframe trend. By discarding outliers it also benefits from not being impacted by brief pumps/volatility, instead responding only to more sustained changes in trend, such as rallies and parabolic moves. In order to give an accurate result the IQR is calculated using a dataset of high, low and hlcc4 values for all bars within the lookback length. Once calculated this value is then halved which, strictly speaking, makes it a semi-interquartile range.
All three of these components can be used individually or summed together to create a hybrid dynamics factor. Furthermore each multiplier can be set to both positive and negative values allowing for some interesting and creative possibilities. An optional smoothing filter can be applied to the sum, this is a basic SWMA-4 which is can reduce the impact of sudden changes but does incur a noticeable lag. Finally, a basic limiter condition has been hard-coded here to prevent the sum total from ever going below zero.
Capping off this section is a pair of direction multipliers. These simply take the prior dynamics sum and allow for further multiplication applied only to one side (uptrend/lo-stop and downtrend/hi-stop). To see why this is useful consider that markets often behave differently in each direction, we've all seen prices steadily climb over several weeks and then abruptly dump in the process of a day or two, shorter time frames are no stranger to this either. A lack of downside liquidity, a panicked market, aggressive shorts. All these things contribute to significant differences in downward price action. This function allows for tighter stops in one direction compared to the other to reflect this imbalance.
VISUALISATIONS
With all of these options and possibilities, some visual aids are useful. Beneath the dynamics' section are several visual options including both sources post-filter and the actual 'bands' created by the dynamics. These are what govern the stop levels and seeing them in full can help to better understand what our various configurations actually do. We can even hide the stop levels altogether and just use the bands, making this a kind of expanded Keltner Channel. Here we can also find colour and opacity settings for everything we've discussed.
EXAMPLES
The obvious first example here is the standard %-change trailing stop loss which, from my experience, tends to be the best suited for lower time frames. Filtering should probably minimal here. In both charts here we use the default config for source inputs, the top is a standard bi-directional setup with 1.5% tsl while the bottom uses a 2.5% tsl with the histop multiplier reduced to 0 resulting in an uptrend only stoploss.
Shown here in grey is the standard Supertrend which uses 'hl2' as centre and 'close' as trigger, ATR(10) multiplied by 3. On top we have the default filtered source config with ATR(8) multiplied by 2 which gives a different yet functionally similar result, below is the same source config instead using IQR(12) multiplied by 2. Notice here the more 'stepped' response from IQR following the central rally, holding back for a while before closing in on price and ultimately initiating reversal much sooner. Unlike ATR, the length parameter for IQR is absolute and can more significantly affect its responsiveness.
Next we focus on the visualisation options, on top we have the default source config with ATR(8) multiplied by 2 and IQR(12) multiplied by 1. Here we have activated the switch to show 'bands', from this we can see the actual summed dynamics and how it influences the stop levels. Below that we have an altogether different config utilising the included filters which are now visible. In this example we have created a basic 8/21 EMA cross and set a 1% TSL, notice the brief fakeout in the middle which ordinarily might indicate a buy signal. Here the TSL functions as an additional requirement which in this case is not met and thus no buy signal is given.
Finally we have a couple of more 'experimental' examples. On top we have Lazybear's 'Variable Moving Average' in white which has been assigned via 'aux' as the centre with no additional filtering, the default config for trigger is used here and a basic TSL of 1.5% added. It's a simple example but it shows how this can be applied to other indicators. At the bottom we return to the default source config, combining a TSL of 8% with IQR(24) multiplied by -2. Note here the negative IQR with greater length which causes the stop to close in on price following significant deviations while otherwise remaining fairly wide. Combining positive and negative multiples of each factor can yield mixed results, some more useful than others depending upon suitable market conditions.
Since this has been quite lengthy, i shall leave it there. Suffice to say that there are plenty more ways to use this besides these examples. Please feel free to share any of your own ideas in the comments below. Enjoy.
CVD - Cumulative Volume Delta (Chart)█ OVERVIEW
This indicator displays cumulative volume delta (CVD) as an on-chart oscillator. It uses intrabar analysis to obtain more precise volume delta information compared to methods that only use the chart's timeframe.
The core concepts in this script come from our first CVD indicator , which displays CVD values as plot candles in a separate indicator pane. In this script, CVD values are scaled according to price ranges and represented on the main chart pane.
█ CONCEPTS
Bar polarity
Bar polarity refers to the position of the close price relative to the open price. In other words, bar polarity is the direction of price change.
Intrabars
Intrabars are chart bars at a lower timeframe than the chart's. Each 1H chart bar of a 24x7 market will, for example, usually contain 60 bars at the lower timeframe of 1min, provided there was market activity during each minute of the hour. Mining information from intrabars can be useful in that it offers traders visibility on the activity inside a chart bar.
Lower timeframes (LTFs)
A lower timeframe is a timeframe that is smaller than the chart's timeframe. This script utilizes a LTF to analyze intrabars, or price changes within a chart bar. The lower the LTF, the more intrabars are analyzed, but the less chart bars can display information due to the limited number of intrabars that can be analyzed.
Volume delta
Volume delta is a measure that separates volume into "up" and "down" parts, then takes the difference to estimate the net demand for the asset. This approach gives traders a more detailed insight when analyzing volume and market sentiment. There are several methods for determining whether an asset's volume belongs in the "up" or "down" category. Some indicators, such as On Balance Volume and the Klinger Oscillator , use the change in price between bars to assign volume values to the appropriate category. Others, such as Chaikin Money Flow , make assumptions based on open, high, low, and close prices. The most accurate method involves using tick data to determine whether each transaction occurred at the bid or ask price and assigning the volume value to the appropriate category accordingly. However, this method requires a large amount of data on historical bars, which can limit the historical depth of charts and the number of symbols for which tick data is available.
In the context where historical tick data is not yet available on TradingView, intrabar analysis is the most precise technique to calculate volume delta on historical bars on our charts. This indicator uses intrabar analysis to achieve a compromise between simplicity and accuracy in calculating volume delta on historical bars. Our Volume Profile indicators use it as well. Other volume delta indicators in our Community Scripts , such as the Realtime 5D Profile , use real-time chart updates to achieve more precise volume delta calculations. However, these indicators aren't suitable for analyzing historical bars since they only work for real-time analysis.
This is the logic we use to assign intrabar volume to the "up" or "down" category:
• If the intrabar's open and close values are different, their relative position is used.
• If the intrabar's open and close values are the same, the difference between the intrabar's close and the previous intrabar's close is used.
• As a last resort, when there is no movement during an intrabar and it closes at the same price as the previous intrabar, the last known polarity is used.
Once all intrabars comprising a chart bar are analyzed, we calculate the net difference between "up" and "down" intrabar volume to produce the volume delta for the chart bar.
█ FEATURES
CVD resets
The "cumulative" part of the indicator's name stems from the fact that calculations accumulate during a period of time. By periodically resetting the volume delta accumulation, we can analyze the progression of volume delta across manageable chunks, which is often more useful than looking at volume delta accumulated from the beginning of a chart's history.
You can configure the reset period using the "CVD Resets" input, which offers the following selections:
• None : Calculations do not reset.
• On a fixed higher timeframe : Calculations reset on the higher timeframe you select in the "Fixed higher timeframe" field.
• At a fixed time that you specify.
• At the beginning of the regular session .
• On trend changes : Calculations reset on the direction change of either the Aroon indicator, Parabolic SAR , or Supertrend .
• On a stepped higher timeframe : Calculations reset on a higher timeframe automatically stepped using the chart's timeframe and following these rules:
Chart TF HTF
< 1min 1H
< 3H 1D
<= 12H 1W
< 1W 1M
>= 1W 1Y
Specifying intrabar precision
Ten options are included in the script to control the number of intrabars used per chart bar for calculations. The greater the number of intrabars per chart bar, the fewer chart bars can be analyzed.
The first five options allow users to specify the approximate amount of chart bars to be covered:
• Least Precise (Most chart bars) : Covers all chart bars by dividing the current timeframe by four.
This ensures the highest level of intrabar precision while achieving complete coverage for the dataset.
• Less Precise (Some chart bars) & More Precise (Less chart bars) : These options calculate a stepped LTF in relation to the current chart's timeframe.
• Very precise (2min intrabars) : Uses the second highest quantity of intrabars possible with the 2min LTF.
• Most precise (1min intrabars) : Uses the maximum quantity of intrabars possible with the 1min LTF.
The stepped lower timeframe for "Less Precise" and "More Precise" options is calculated from the current chart's timeframe as follows:
Chart Timeframe Lower Timeframe
Less Precise More Precise
< 1hr 1min 1min
< 1D 15min 1min
< 1W 2hr 30min
> 1W 1D 60min
The last five options allow users to specify an approximate fixed number of intrabars to analyze per chart bar. The available choices are 12, 24, 50, 100, and 250. The script will calculate the LTF which most closely approximates the specified number of intrabars per chart bar. Keep in mind that due to factors such as the length of a ticker's sessions and rounding of the LTF, it is not always possible to produce the exact number specified. However, the script will do its best to get as close to the value as possible.
As there is a limit to the number of intrabars that can be analyzed by a script, a tradeoff occurs between the number of intrabars analyzed per chart bar and the chart bars for which calculations are possible.
Display
This script displays raw or cumulative volume delta values on the chart as either line or histogram oscillator zones scaled according to the price chart, allowing traders to visualize volume activity on each bar or cumulatively over time. The indicator's background shows where CVD resets occur, demarcating the beginning of new zones. The vertical axis of each oscillator zone is scaled relative to the one with the highest price range, and the oscillator values are scaled relative to the highest volume delta. A vertical offset is applied to each oscillator zone so that the highest oscillator value aligns with the lowest price. This method ensures an accurate, intuitive visual comparison of volume activity within zones, as the scale is consistent across the chart, and oscillator values sit below prices. The vertical scale of oscillator zones can be adjusted using the "Zone Height" input in the script settings.
This script displays labels at the highest and lowest oscillator values in each zone, which can be enabled using the "Hi/Lo Labels" input in the "Visuals" section of the script settings. Additionally, the oscillator's value on a chart bar is displayed as a tooltip when a user hovers over the bar, which can be enabled using the "Value Tooltips" input.
Divergences occur when the polarity of volume delta does not match that of the chart bar. The script displays divergences as bar colors and background colors that can be enabled using the "Color bars on divergences" and "Color background on divergences" inputs.
An information box in the lower-left corner of the indicator displays the HTF used for resets, the LTF used for intrabars, the average quantity of intrabars per chart bar, and the number of chart bars for which there is LTF data. This is enabled using the "Show information box" input in the "Visuals" section of the script settings.
FOR Pine Script™ CODERS
• This script utilizes `ltf()` and `ltfStats()` from the lower_tf library.
The `ltf()` function determines the appropriate lower timeframe from the selected calculation mode and chart timeframe, and returns it in a format that can be used with request.security_lower_tf() .
The `ltfStats()` function, on the other hand, is used to compute and display statistical information about the lower timeframe in an information box.
• The script utilizes display.data_window and display.status_line to restrict the display of certain plots.
These new built-ins allow coders to fine-tune where a script’s plot values are displayed.
• The newly added session.isfirstbar_regular built-in allows for resetting the CVD segments at the start of the regular session.
• The VisibleChart library developed by our resident PineCoders team leverages the chart.left_visible_bar_time and chart.right_visible_bar_time variables to optimize the performance of this script.
These variables identify the opening time of the leftmost and rightmost visible bars on the chart, allowing the script to recalculate and draw objects only within the range of visible bars as the user scrolls.
This functionality also enables the scaling of the oscillator zones.
These variables are just a couple of the many new built-ins available in the chart.* namespace.
For more information, check out this blog post or look them up by typing "chart." in the Pine Script™ Reference Manual .
• Our ta library has undergone significant updates recently, including the incorporation of the `aroon()` indicator used as a method for resetting CVD segments within this script.
Revisit the library to see more of the newly added content!
Look first. Then leap.
libcompressLibrary "libcompress"
numbers compressor for large output data compression
compress_fp24()
converts float to base64 (4 chars) | 24 bits: 1 sign + 5 exponent + 18 mantissa
Returns: 4-character base64_1/5/18 representation of x
compress_ufp18()
converts unsigned float to base64 (3 chars) | 18 bits: 5 exponent + 13 mantissa
Returns: 3-character base64_0/5/13 representation of x
compress_int()
converts int to base64
Intrabar Efficiency Ratio█ OVERVIEW
This indicator displays a directional variant of Perry Kaufman's Efficiency Ratio, designed to gauge the "efficiency" of intrabar price movement by comparing the sum of movements of the lower timeframe bars composing a chart bar with the respective bar's movement on an average basis.
█ CONCEPTS
Efficiency Ratio (ER)
Efficiency Ratio was first introduced by Perry Kaufman in his 1995 book, titled "Smarter Trading". It is the ratio of absolute price change to the sum of absolute changes on each bar over a period. This tells us how strong the period's trend is relative to the underlying noise. Simply put, it's a measure of price movement efficiency. This ratio is the modulator utilized in Kaufman's Adaptive Moving Average (KAMA), which is essentially an Exponential Moving Average (EMA) that adapts its responsiveness to movement efficiency.
ER's output is bounded between 0 and 1. A value of 0 indicates that the starting price equals the ending price for the period, which suggests that price movement was maximally inefficient. A value of 1 indicates that price had travelled no more than the distance between the starting price and the ending price for the period, which suggests that price movement was maximally efficient. A value between 0 and 1 indicates that price had travelled a distance greater than the distance between the starting price and the ending price for the period. In other words, some degree of noise was present which resulted in reduced efficiency over the period.
As an example, let's say that the price of an asset had moved from $15 to $14 by the end of a period, but the sum of absolute changes for each bar of data was $4. ER would be calculated like so:
ER = abs(14 - 15)/4 = 0.25
This suggests that the trend was only 25% efficient over the period, as the total distanced travelled by price was four times what was required to achieve the change over the period.
Intrabars
Intrabars are chart bars at a lower timeframe than the chart's. Each 1H chart bar of a 24x7 market will, for example, usually contain 60 intrabars at the LTF of 1min, provided there was market activity during each minute of the hour. Mining information from intrabars can be useful in that it offers traders visibility on the activity inside a chart bar.
Lower timeframes (LTFs)
A lower timeframe is a timeframe that is smaller than the chart's timeframe. This script determines which LTF to use by examining the chart's timeframe. The LTF determines how many intrabars are examined for each chart bar; the lower the timeframe, the more intrabars are analyzed, but fewer chart bars can display indicator information because there is a limit to the total number of intrabars that can be analyzed.
Intrabar precision
The precision of calculations increases with the number of intrabars analyzed for each chart bar. As there is a 100K limit to the number of intrabars that can be analyzed by a script, a trade-off occurs between the number of intrabars analyzed per chart bar and the chart bars for which calculations are possible.
Intrabar Efficiency Ratio (IER)
Intrabar Efficiency Ratio applies the concept of ER on an intrabar level. Rather than comparing the overall change to the sum of bar changes for the current chart's timeframe over a period, IER compares single bar changes for the current chart's timeframe to the sum of absolute intrabar changes, then applies smoothing to the result. This gives an indication of how efficient changes are on the current chart's timeframe for each bar of data relative to LTF bar changes on an average basis. Unlike the standard ER calculation, we've opted to preserve directional information by not taking the absolute value of overall change, thus allowing it to be utilized as a momentum oscillator. However, by taking the absolute value of this oscillator, it could potentially serve as a replacement for ER in the design of adaptive moving averages.
Since this indicator preserves directional information, IER can be regarded as similar to the Chande Momentum Oscillator (CMO) , which was presented in 1994 by Tushar Chande in "The New Technical Trader". Both CMO and ER essentially measure the same relationship between trend and noise. CMO simply differs in scale, and considers the direction of overall changes.
█ FEATURES
Display
Three different display types are included within the script:
• Line : Displays the middle length MA of the IER as a line .
Color for this display can be customized via the "Line" portion of the "Visuals" section in the script settings.
• Candles : Displays the non-smooth IER and two moving averages of different lengths as candles .
The `open` and `close` of the candle are the longest and shortest length MAs of the IER respectively.
The `high` and `low` of the candle are the max and min of the IER, longest length MA of the IER, and shortest length MA of the IER respectively.
Colors for this display can be customized via the "Candles" portion of the "Visuals" section in the script settings.
• Circles : Displays three MAs of the IER as circles .
The color of each plot depends on the percent rank of the respective MA over the previous 100 bars.
Different colors are triggered when ranks are below 10%, between 10% and 50%, between 50% and 90%, and above 90%.
Colors for this display can be customized via the "Circles" portion of the "Visuals" section in the script settings.
With either display type, an optional information box can be displayed. This box shows the LTF that the script is using, the average number of lower timeframe bars per chart bar, and the number of chart bars that contain LTF data.
Specifying intrabar precision
Ten options are included in the script to control the number of intrabars used per chart bar for calculations. The greater the number of intrabars per chart bar, the fewer chart bars can be analyzed.
The first five options allow users to specify the approximate amount of chart bars to be covered:
• Least Precise (Most chart bars) : Covers all chart bars by dividing the current timeframe by four.
This ensures the highest level of intrabar precision while achieving complete coverage for the dataset.
• Less Precise (Some chart bars) & More Precise (Less chart bars) : These options calculate a stepped LTF in relation to the current chart's timeframe.
• Very precise (2min intrabars) : Uses the second highest quantity of intrabars possible with the 2min LTF.
• Most precise (1min intrabars) : Uses the maximum quantity of intrabars possible with the 1min LTF.
The stepped lower timeframe for "Less Precise" and "More Precise" options is calculated from the current chart's timeframe as follows:
Chart Timeframe Lower Timeframe
Less Precise More Precise
< 1hr 1min 1min
< 1D 15min 1min
< 1W 2hr 30min
> 1W 1D 60min
The last five options allow users to specify an approximate fixed number of intrabars to analyze per chart bar. The available choices are 12, 24, 50, 100, and 250. The script will calculate the LTF which most closely approximates the specified number of intrabars per chart bar. Keep in mind that due to factors such as the length of a ticker's sessions and rounding of the LTF, it is not always possible to produce the exact number specified. However, the script will do its best to get as close to the value as possible.
Specifying MA type
Seven MA types are included in the script for different averaging effects:
• Simple
• Exponential
• Wilder (RMA)
• Weighted
• Volume-Weighted
• Arnaud Legoux with `offset` and `sigma` set to 0.85 and 6 respectively.
• Hull
Weighting
This script includes the option to weight IER values based on the percent rank of absolute price changes on the current chart's timeframe over a specified period, which can be enabled by checking the "Weigh using relative close changes" option in the script settings. This places reduced emphasis on IER values from smaller changes, which may help to reduce noise in the output.
█ FOR Pine Script™ CODERS
• This script imports the recently published lower_ltf library for calculating intrabar statistics and the optimal lower timeframe in relation to the current chart's timeframe.
• This script uses the recently released request.security_lower_tf() Pine Script™ function discussed in this blog post .
It works differently from the usual request.security() in that it can only be used on LTFs, and it returns an array containing one value per intrabar.
This makes it much easier for programmers to access intrabar information.
• This script implements a new recommended best practice for tables which works faster and reduces memory consumption.
Using this new method, tables are declared only once with var , as usual. Then, on the first bar only, we use table.cell() to populate the table.
Finally, table.set_*() functions are used to update attributes of table cells on the last bar of the dataset.
This greatly reduces the resources required to render tables.
Look first. Then leap.
Quantitative Backtesting Panel + ROI Table - ShortsThis script is an aggregate of a backtesting panel with quantitative metrics, ROI table and open ROI reader. It also contains a mechanism for having a fixed percentage stop loss, similar to native TV backtester. For shorts only.
Backtesting Panel:
- Certain metrics are color coded, with green being good performance, orange being neutral, red being undesirable.
• ROI : return with the system, in %
• ROI(COMP=1): return if money is compounded at a rate of 100%
• Hit rate: accuracy of the system, as a %
• Profit factor: gross profit/gross loss
• Maximum drawdown: the maximum value from a peak to a successive trough of the system's equity curve
• MAE: Maximum Adverse Excursion. The biggest loss of a trade suffered while the position is still open
• Total trades: total number of closed trades
• Max gain/max loss: shows the biggest win over the biggest loss suffered
• Sharpe ratio: measures the performance of the system with adjusted risk (no comparison to risk-free asset)
• CAGR: Compound Annual Growth Rate. The mean annual rate of growth of the system of n years (provided n>1)
• Kurtosis: measures how heavily the tails of the distribution differ from that of a normal distribution (symmetric on both sides of mean where mean=0, standard deviation=1). A normal distribution has a kurtosis of 3, and skewness of 0. The kurtosis indicates whether or not the tails of the returns contain extreme values
• Skewness: measures the symmetry of the distribution of returns
- Leptokurtic: K > 0. Having more kurtosis than a normal distribution. It's stretched up and to the side too (2nd pic down). High kurtosis (leptokurtic) is bad as the wider tails (called heavy tails) suggest there is relatively high probability of extreme events
- Mesokurtic: K =0. Having the same kurtosis as a normal distribution
- Platykurtic: K < 0. Having less kurtosis than a normal distribution. This suggests there are light tails and fewer extreme events in the distribution
- Skewness is good: +/- 0.5 (fairly symmetrical)
- Skewness is average: -1 to -0.5 or 0.5 to 1 (moderately skewed)
- Skewness is bad: > +/- 1 (highly skewed)
Evolving ROI table:
- The table of ROI values evolve with the year and month. The sum of each year is given. Please avoid using it on non-cryptocurrencies or any market whose trading session is not 24/7
Open ROI reader:
- At the top center is the open ROI of a trade
Quantitative Backtesting Panel + ROI Table - LongsThis script is an aggregate of a backtesting panel with quantitative metrics, ROI table and open ROI reader. It also contains a mechanism for having a fixed percentage stop loss, similar to native TV backtester. For longs only.
Backtesting Panel:
- Certain metrics are color coded, with green being good performance, orange being neutral, red being undesirable.
• ROI : return with the system, in %
• ROI(COMP=1): return if money is compounded at a rate of 100%
• Hit rate: accuracy of the system, as a %
• Profit factor: gross profit/gross loss
• Maximum drawdown: the maximum value from a peak to a successive trough of the system's equity curve
• MAE: Maximum Adverse Excursion. The biggest loss of a trade suffered while the position is still open
• Total trades: total number of closed trades
• Max gain/max loss: shows the biggest win over the biggest loss suffered
• Sharpe ratio: measures the performance of the system with adjusted risk (no comparison to risk-free asset)
• CAGR: Compound Annual Growth Rate. The mean annual rate of growth of the system of n years (provided n>1)
• Kurtosis: measures how heavily the tails of the distribution differ from that of a normal distribution (symmetric on both sides of mean where mean=0, standard deviation=1). A normal distribution has a kurtosis of 3, and skewness of 0. The kurtosis indicates whether or not the tails of the returns contain extreme values
• Skewness: measures the symmetry of the distribution of returns
- Leptokurtic: K > 0. Having more kurtosis than a normal distribution. It's stretched up and to the side too (2nd pic down). High kurtosis (leptokurtic) is bad as the wider tails (called heavy tails) suggest there is relatively high probability of extreme events
- Mesokurtic: K =0. Having the same kurtosis as a normal distribution
- Platykurtic: K < 0. Having less kurtosis than a normal distribution. This suggests there are light tails and fewer extreme events in the distribution
- Skewness is good: +/- 0.5 (fairly symmetrical)
- Skewness is average: -1 to -0.5 or 0.5 to 1 (moderately skewed)
- Skewness is bad: > +/- 1 (highly skewed)
Evolving ROI table:
- The table of ROI values evolve with the year and month. The sum of each year is given. Please avoid using it on non-cryptocurrencies or any market whose trading session is not 24/7
Open ROI reader:
- At the top center is the open ROI of a trade
Fed Net Liquidity Indicator (24-Oct-2022 update)This indicator is an implementation of the USD Liquidity Index originally proposed by Arthur Hayes based on the initial implementation of jlb05013, kudos to him!
I have incorporated subsequent additions (Standing Repo Facility and Central Bank Liquidity Swaps lines) and dealt with some recent changes in reporting units from TradingView.
This is a macro indicator that aims at tracking how much USD liquidity is available to chase financial assets:
- When the FED is expanding liquidity, financial asset prices tend to increase
- When the FED is contracting liquidity, financial asset prices tend to decrease
Here is the current calculation:
Net Liquidity =
(+) The Fed’s Balance Sheet (FRED:WALCL)
(-) NY Fed Total Amount of Accepted Reverse Repo Bids (FRED:RRPONTTLD)
(-) US Treasury General Account Balance Held at NY Fed (FRED:WTREGEN)
(+) NY Fed - Standing Repo Facility (FRED:RPONTSYD)
(+) NY Fed - Central Bank Liquidity Swaps (FRED:SWPT)
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
Boyle Trinomial Options Pricing Model [Loxx]Boyle Trinomial Options Pricing Model is an options pricing indicator that builds an N-order trinomial tree to price American and European options. This is different form the Binomial model in that the Binomial assumes prices can only go up and down wheres the Trinomial model assumes prices can go up, down, or sideways (shoutout to the "crab" market enjoyers). This method also allows for dividend adjustment.
The Trinomial Tree via VinegarHill Finance Labs
A two-jump process for the asset price over each discrete time step was developed in the binomial lattice. Boyle expanded this frame of reference and explored the feasibility of option valuation by allowing for an extra jump in the stochastic process. In keeping with Black Scholes, Boyle examined an asset (S) with a lognormal distribution of returns. Over a small time interval, this distribution can be approximated by a three-point jump process in such a way that the expected return on the asset is the riskless rate, and the variance of the discrete distribution is equal to the variance of the corresponding lognormal distribution. The three point jump process was introduced by Phelim Boyle (1986) as a trinomial tree to price options and the effect has been momentous in the finance literature. Perhaps shamrock mythology or the well-known ballad associated with Brendan Behan inspired the Boyle insight to include a third jump in lattice valuation. His trinomial paper has spawned a huge amount of ground breaking research. In the trinomial model, the asset price S is assumed to jump uS or mS or dS after one time period (dt = T/n), where u > m > d. Joshi (2008) point out that the trinomial model is characterized by the following five parameters: (1) the probability of an up move pu, (2) the probability of an down move pd, (3) the multiplier on the stock price for an up move u, (4) the multiplier on the stock price for a middle move m, (5) the multiplier on the stock price for a down move d. A recombining tree is computationally more efficient so we require:
ud = m*m
M = exp (r∆t),
V = exp (σ 2∆t),
dt or ∆t = T/N
where where N is the total number of steps of a trinomial tree. For a tree to be risk-neutral, the mean and variance across each time steps must be asymptotically correct. Boyle (1986) chose the parameters to be:
m = 1, u = exp(λσ√ ∆t), d = 1/u
pu =( md − M(m + d) + (M^2)*V )/ (u − d)(u − m) ,
pd =( um − M(u + m) + (M^2)*V )/ (u − d)(m − d)
Boyle suggested that the choice of value for λ should exceed 1 and the best results were obtained when λ is approximately 1.20. One approach to constructing trinomial trees is to develop two steps of a binomial in combination as a single step of a trinomial tree. This can be engineered with many binomials CRR(1979), JR(1979) and Tian (1993) where the volatility is constant.
Further reading:
A Lattice Framework for Option Pricing with Two State
Trinomial tree via wikipedia
Inputs
Spot price: select from 33 different types of price inputs
Calculation Steps: how many iterations to be used in the Trinomial model. In practice, this number would be anywhere from 5000 to 15000, for our purposes here, this is limited to 220.
Strike Price: the strike price of the option you're wishing to model
Market Price: this is the market price of the option; choose, last, bid, or ask to see different results
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Trinomial model, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option
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
Included
Option pricing panel
Loxx's Expanded Source Types
Related indicators
Implied Volatility Estimator using Black Scholes
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Implied Volatility Estimator using Black Scholes [Loxx]Implied Volatility Estimator using Black Scholes derives a estimation of implied volatility using the Black Scholes options pricing model. The Bisection algorithm is used for our purposes here. This includes the ability to adjust for dividends.
Implied Volatility
The implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of that option. The VIX , in contrast, is a model-free estimate of Implied Volatility. The latter is viewed as being important because it represents a measure of risk for the underlying asset. Elevated Implied Volatility suggests that risks to underlying are also elevated. Ordinarily, to estimate implied volatility we rely upon Black-Scholes (1973). This implies that we are prepared to accept the assumptions of Black Scholes (1973).
Inputs
Spot price: select from 33 different types of price inputs
Strike Price: the strike price of the option you're wishing to model
Market Price: this is the market price of the option; choose, last, bid, or ask to see different results
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Bisection algo, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option
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 algorithm inputs for low and high aren't to be changed unless you're working through the mathematics of how Bisection works.
Included
Option pricing panel
Loxx's Expanded Source Types
Related Indicators
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model [Loxx]Cox-Ross-Rubinstein Binomial Tree Options Pricing Model is an options pricing panel calculated using an N-iteration (limited to 300 in Pine Script due to matrices size limits) "discrete-time" (lattice based) method to approximate the closed-form Black–Scholes formula. Joshi (2008) outlined varying binomial options pricing model furnishes a numerical approach for the valuation of options. Significantly, the American analogue can be estimated using the binomial tree. This indicator is the complex calculation for Binomial option pricing. Most folks take a shortcut and only calculate 2 iterations. I've coded this to allow for up to 300 iterations. This can be used to price American Puts/Calls and European Puts/Calls. I'll be updating this indicator will be updated with additional features over time. If you would like to learn more about options, I suggest you check out the book textbook Options, Futures and other Derivative by John C Hull.
***This indicator only works on the daily timeframe!***
A quick graphic of what this all means:
In the graphic, "n" are the steps, in this case we can do up to 300, in production we'd need to do 5-15K. That's a lot of steps! You can see here how the binomial tree fans out. As I said previously, most folks only calculate 2 steps, here we are calculating up to 300.
Want to learn more about Simple Introduction to Cox, Ross Rubinstein (1979) ?
Watch this short series "Introduction to Basic Cox, Ross and Rubinstein (1979) model."
Limitations of Black Scholes options pricing model
This is a widely used and well-known options pricing model, factors in current stock price, options strike price, time until expiration (denoted as a percent of a year), and risk-free interest rates. The Black-Scholes Model is quick in calculating any number of option prices. But the model cannot accurately calculate American options, since it only considers the price at an option's expiration date. American options are those that the owner may exercise at any time up to and including the expiration day.
What are Binomial Trees in options pricing?
A useful and very popular technique for pricing an option involves constructing a binomial tree. This is a diagram representing different possible paths that might be followed by the stock price over the life of an option. The underlying assumption is that the stock price follows a random walk. In each time step, it has a certain probability of moving up by a certain percentage amount and a certain probability of moving down by a certain percentage amount. In the limit, as the time step becomes smaller, this model is the same as the Black–Scholes–Merton model.
What is the Binomial options pricing model ?
This model uses a tree diagram with volatility factored in at each level to show all possible paths an option's price can take, then works backward to determine one price. The benefit of the Binomial Model is that you can revisit it at any point for the possibility of early exercise. Early exercise is executing the contract's actions at its strike price before the contract's expiration. Early exercise only happens in American-style options. However, the calculations involved in this model take a long time to determine, so this model isn't the best in rushed situations.
What is the Cox-Ross-Rubinstein Model?
The Cox-Ross-Rubinstein binomial model can be used to price European and American options on stocks without dividends, stocks and stock indexes paying a continuous dividend yield, futures, and currency options. Option pricing is done by working backwards, starting at the terminal date. Here we know all the possible values of the underlying price. For each of these, we calculate the payoffs from the derivative, and find what the set of possible derivative prices is one period before. Given these, we can find the option one period before this again, and so on. Working ones way down to the root of the tree, the option price is found as the derivative price in the first node.
Inputs
Spot price: select from 33 different types of price inputs
Calculation Steps: how many iterations to be used in the Binomial 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 CRRBT 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
Take notes:
Futures don't risk free yields. If you are pricing options of futures, then the risk-free rate is zero.
Dividend yields are calculated using TradingView's internal dividend values
This indicator only works on the daily timeframe
Included
Option pricing panel
Loxx's Expanded Source Types
Bull/Bear Candle % Oscillator█ OVERVIEW
This script determines the proportion of bullish and bearish candles in a given sample size. It will produce an oscillator that fluctuates between 100 and -100, where values > 0 indicate more bullish candles in the sample and values < 0 indicate more bearish candles in the sample. Data produced by this oscillator is normalized around the 50% value, meaning that an even 50/50 split between bullish and bearish candles makes this oscillator produce 0; this oscillator indirectly represents the percent proportion of bullish and bearish candles in the sample (see HOW TO USE/INTERPRETATION OF DATA ).
It has two overarching settings: 'classic' and 'range'.
█ CONCEPTS
This script will cover concepts related to candlestick analysis, volumetric analysis, and lower timeframes.
Candlestick Analysis - The idea behind this script is to solely look at the candlesticks themselves and derive information from them in a given sample. It separates candles into two categories, bullish (close > open) and bearish (close < open).
If the indicator's setting is set to 'classic', the size of candles do not matter and all are assigned a value of 1 or 0.
If the indicator's setting is set to 'range', specific candle ranges modify the proportion of bullish/bearish values. Bullish candle values include all bullish candles in the set from their lows to the close, plus the lower wicks of all bearish candles. Bearish candle values include all bearish candles in the set from their highs to the close, plus the upper wicks of all bullish candles.
Volumetric Analysis - One of this script's features allows the user to modify the bullish and bearish candle proportions by its 'weight' determined by its volume compared to the sample set's total volume. Volumetric analysis for the 'range' setting are more complex than 'classic' as described below.
Lower Timeframes - For volumetric analysis to be done on candle wicks, there needed to be a way to determine how much volume had occurred in the wick by itself to find the weight of upper and lower wicks. To accomplish this, I employed PineScrypt's request.security_lower_tf function to grab OHLC values of lower timeframe candles (as well as volume) to determine how much volume had occurred in the wicks of the chart resolution's candle. The default OHLC values used here are the lows for upper wicks and highs for lower wicks. These OHLC values are then compared to the chart resolution candle's close to determine if the volume of that lower timeframe candle should be shifted to the wick weight or stay in the current weight of that candle. The reason 'low' and 'high' are used here is to guarantee that 100% of the volume of a lower timeframe candle had occurred in the wick of the candle at the current resolution (see LIMITATIONS ).
Bullish candles will exclude volume of all lower timeframe candles whose lows were greater than that candle's close. Bearish candles will exclude volume of all lower timeframe candles whose highs were less than that candle's close. These wick volumes are then divided by the volume of the sample set, and wick sizes are then multiplied by this weight before being added to their specific bullish/bearish sums (lower wicks to bullish and upper wicks to bearish).
█ FEATURES
There are 13 inputs for the user to modify the behavior/visual representation of this script.
Sample Length - This determines how many candles are in the sample set to find the proportion of bullish and bearish candles.
Colors and Invert Colors - There are three colors set by the user: a bullish color, neutral color, and bearish color. The oscillator plots two lines, one at 0 and another that represents the proportion of bullish or bearish candles in the sample set (we'll call this the 'signal line'). If the oscillator is above 0, bullish color is used, bearish otherwise. This script generates a gradient to color a filled area between the 0 line and the signal line based on the historical values of the oscillator itself and the signal line. For bullish values, the closer the signal line is to the max (or restricted max described below) that the oscillator has experienced, the more colored toward bullish color the shaded area will be, using the neutral color as a starting point. The same is applied to the bearish values using the bearish color.
There is an additional input to invert the colors so that the bearish color is associated with bullish values and vise-versa.
Calculation Type - This determines the overarching behavior of the oscillator and has two settings:
Classic - The weight of candles are either 1 if they occurred and 0 if not.
Range - The weight of candles is determined by the size of specific sections as described in CONCEPTS - Candlestick Analysis .
Volume Weighted - This enables modifying the weights of candles as described in CONCEPTS - Volumetric Analysis and Lower Timeframes based on which Calculation Type is used.
Wick Slice Resolution - This is the lower timeframe resolution that will be used to slice the chart resolution's candle when determining the volumetric weight of wicks. Lower timeframe resolutions like '1 minute' will yield more precise results as they will give more data points to go off of (see LIMITATIONS ).
Upper/Lower Wick Source - These two inputs allow the user to select which OHLC values to compare against the chart resolution's candle close when determining which lower timeframe candles will have their volumes associated with the wicks of candles being analyzed at the chart's resolution.
Restrict Min/Max Data and Restriction - This will restrict the maximum and minimum values that will be used for the signal line when comparing its value to previous oscillator values and change how the color gradient is generated for the indicator. Restriction is the number of candles back that will determine these maximum and minimum values.
Display Min/Max Guide - This will plot two lines that are colored the corresponding bullish and bearish colors which follow what the maximum and minimum values are currently for the oscillator.
█ HOW TO USE/INTERPRETATION OF DATA
As mentioned in the OVERVIEW section, this oscillator provides an indirect representation of the percent proportion of bullish or bearish candles in a given sample. If the oscillator reads 80, this does not mean that 80% of all candles in the sample were bullish . To find the percentage of candles that were bullish or bearish, the user needs to perform the following:
50% + ((|oscillator value| / 100) * 50)%
If the oscillator value is negative, the value from above will represent the percentage of bearish candles in the sample. If it is positive, this value represents the percentage of bullish candles in the sample.
Example 1 (oscillator value = 80):
50% + ((|80| / 100) * 50)%
50% + ((0.80) * 50)%
50% + 40% = 90%
90% of the candles in the sample were bullish.
Example 2 (oscillator value = -43):
50% + ((|-43| / 100) * 50)%
50% + ((0.43) * 50)%
50% + 21.5% = 71.5%
71.5% of the candles in the sample were bearish.
An example use of this indicator would be to put in a 'buy' order when its value shows a significant proportion of the sampled candles were bearish, and put in a 'sell' order when a significant proportion of candles were bullish. Potential divergences of this oscillator may also be used to plan trades accordingly such as bearish divergence - price continues higher as the oscillator decreases in value and vise-versa.*
* Nothing in this script constitutes any form of financial advice. The user is solely responsible for their trading decisions and I will not be held liable for any losses or gains incurred with the use of this script. Please proceed with caution when using this script to assist with trading decisions.
█ LIMITATIONS
Range Volumetric Weights :
Because of the conditions that must be met in order for volume to be considered part of wicks, it is possible that the default settings and their intended reasoning will not produce reliable results. If all lower timeframe candles have highs or lows that are within the body of the candle at the chart's resolution, the volume for the wicks will effectively be 0, which is not an accurate representation of those wicks. This is one of the reasons why I included the ability to change the source values used for these conditions as certain OHLC values may produce more reliable/intended results under these conditions.
Wick Slice Resolution :
PineScript restricts the number of intrabar references to 100,000 total. This script uses 3 separate request.security_lower_tf calls and has a default resolution of 1 minute. This means that if the user were to set the oscillator to the Range setting, enable volume weighted, and had the Wick Slice Resolution set to 1 minute, this script will exceed this 100,000 reference restriction within 24 days of data and will not produce any results beyond the previous 23.14 days.
Below are example uses of all the different settings of this script, these are done on the 1D chart of COINBASE:BTCUSD :
Default Settings:
Classic - Volume Weighted:
Range - no Volume Weight:
Range - Volume Weighted (1 min slices):
Range - Volume Weighted (1 hour slices):
Display Min/Max Guide - No Restriction:
Display Min/Max Guide - Restriction:
Invert Colors:
DCA After Downtrend v2 (by BHD_Trade_Bot)The purpose of the strategy is to identify the end of a short-term downtrend . So that you can easily to DCA certain amount of money for each month.
ENTRY
The buy orders are placed on a monthly basis for assets at the end of a short-term downtrend:
- Each month condition: In 1-hour time frame, each month has 24 * 30 candles
- The end of short-term downtrend condition: use MACD for less delay
CLOSE
The sell orders are placed when:
- Is last bar
The strategy use $1000 and trading fee is 1.1% for each order.
Pro tip: The 1-hour time frame has the best results on average:
- Total spent: $1000 x 33 = $33,000
- Total profit: $65,578
Jathuko Boncu Serok Cendolserok brrooo....
Jakarta - Celsius Network LLC menggugat mantan manajer investasinya, Jason Stone pada selasa lalu. Perusahaan pemberi pinjaman kripto ini menuduh Stone mencuri aset puluhan juta dolar sebelum bangkrut bulan lalu.
Dalam pengaduan yang diajukan di pengadilan kebangkrutan Manhattan, Celsius menuduh Stone dan perusahaannya KeyFi Inc melakukan kelalaian fatal. Stone juga dituduh tidak berkompeten dalam berinvestasi kripto.
Dikutip dari Reuters, Rabu (24/8/2022), Celsius mengatakan Stone terbukti gagal memberikan untung dan menyebabkan kerugian puluhan juta dolar.
Baca artikel detikfinance, "Diduga Tilep Kripto Puluhan Juta Dolar, Manajer Ini Digugat Perusahaannya" selengkapnya
iBox, Initial Balance | IB High, Low, Midpoint | OpeningThis Indicator will print basically 4 lines.
You have to understand the importance of the "Initial Balance" the first trading hour of Cash session is very important in trading stocks and indizes.
So you will get 4 lines:
Opening
Initial Balance High
Initial Balance Low
Initial Balance Midpoint/Halfback
Most indicators for Range Box, Opening Trade, Opening Range, Initial Balance, iBOX and "Ultimate Lines" will only use the timezone of the exchange or your own timezone. I'm living in europe and we have this daylight saving time change in Summer/Winter - which will cause problems with most of the existing indicators or at least will push you to change the times regularly.
Another important point: I really like to switch the indizes when trading on my mobile. So what will happen when you set up opening range for DAX at 09:00 and then switch to S&P500? All indicators I tried failed here - they will just draw a wrong line for SPX, NDX, DJI, FTSE, ASX etc. I fixed that and hard coded stock exchanges and ticker symbols into 3 main groups Initial Balance EU/US/Asia
For example we take DAX - XETRA DAX is opening at 09:00 MEZ (Europe/Berlin)
The Initial Balance is set during the H1 Candle from 09:00 - 09:59
Please be aware, that some cash indizes only deliver data to TradingView after the "opening auction" - so for Xetra DAX you have to book live data and often you will only see data at 09:02/09:03 after the opening auction.
So you will get different opening lines compared from cash to future or your CFD provider. Future and CFD should fit for 99%
The Opening Line will be drawn at exactly 09:00
IB High on the highest price during the H1 candle
IB Low on the lowest price during the H1 candle
IB Halfback is simple: (IB High + IB Low) / 2
The lines will be drawn from cash start until next day and will end 2 minutes before the next cash session will start again. Please make your own experience! Activate the indicator for a CFD or Future switch to M15 and watch the wicks around the 4 lines. Even in the night or the next morning before the next Initial Balance will be set.
For me the lines are valid for around 24 hours and often longer. That's why it's good to have the old lines on the chart too.
To-do:
Yesterday high / low / close / halfback (also for last week and month)
Labels for the lines - sometimes only the colors will confuse you - a simple label should be a benefit (IB_h, IB_l, IB_1/2, 1D_o)
Range Lines for Asia Range and Premarket Range - additionaly a parameter to disable premarket lines when premarket is trading in asia range.
Add Alert condition to get alerts after IB is set
If you have and thoughts, ideas or improvements, please send me an message or leave an comment!
Like i said, the stock exchanges and ticker symbols are hard coded and can be extended for all relevant assets.
Have fun and i really hope this indicator will help improving your trading experience!
Rsi/W%R/Stoch/Mfi: HTF overlay mini-plotsOverlay mini-plots for various indicators. Shows current timeframe; and option to plot 2x higher timeframes (i.e. 15min and 60min on the 5min chart above).
The idea is to de-clutter chart when you just want real-time snippets for an indicator.
Useful for gauging overbought/oversold, across timeframes, at a glance.
~~Indicators~~
~RSI: Relative strength index
~W%R: Williams percent range
~Stochastic
~MFI: Money flow index
~~Inputs~~
~indicator length (NB default is set to 12, NOT the standard 14)
~choose 2x HTFs, show/hide HTF plots
~choose number of bars to show (current timeframe only; HTF plots show only 6 bars)
~horizontal position: offset (bars); shift plots right or left. Can be negative
~vertical position: top/middle/bottom
~other formatting options (color, line thickness, show/hide labels, 70/30 lines, 80/20 lines)
~~tips~~
~should be relatively easy to add further indicators, so long as they are 0-100 based; by editing lines 9 and 11
~change the vertical compression of the plots by playing around with the numbers (+100, -400, etc) in lines 24 and 25
Normalized, Variety, Fast Fourier Transform Explorer [Loxx]Normalized, Variety, Fast Fourier Transform Explorer demonstrates Real, Cosine, and Sine Fast Fourier Transform algorithms. This indicator can be used as a rule of thumb but shouldn't be used in trading.
What is the Discrete Fourier Transform?
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle.
What is the Complex Fast Fourier Transform?
The complex Fast Fourier Transform algorithm transforms N real or complex numbers into another N complex numbers. The complex FFT transforms a real or complex signal x in the time domain into a complex two-sided spectrum X in the frequency domain. You must remember that zero frequency corresponds to n = 0, positive frequencies 0 < f < f_c correspond to values 1 ≤ n ≤ N/2 −1, while negative frequencies −fc < f < 0 correspond to N/2 +1 ≤ n ≤ N −1. The value n = N/2 corresponds to both f = f_c and f = −f_c. f_c is the critical or Nyquist frequency with f_c = 1/(2*T) or half the sampling frequency. The first harmonic X corresponds to the frequency 1/(N*T).
The complex FFT requires the list of values (resolution, or N) to be a power 2. If the input size if not a power of 2, then the input data will be padded with zeros to fit the size of the closest power of 2 upward.
What is Real-Fast Fourier Transform?
Has conditions similar to the complex Fast Fourier Transform value, except that the input data must be purely real. If the time series data has the basic type complex64, only the real parts of the complex numbers are used for the calculation. The imaginary parts are silently discarded.
What is the Real-Fast Fourier Transform?
In many applications, the input data for the DFT are purely real, in which case the outputs satisfy the symmetry
X(N-k)=X(k)
and efficient FFT algorithms have been designed for this situation (see e.g. Sorensen, 1987). One approach consists of taking an ordinary algorithm (e.g. Cooley–Tukey) and removing the redundant parts of the computation, saving roughly a factor of two in time and memory. Alternatively, it is possible to express an even-length real-input DFT as a complex DFT of half the length (whose real and imaginary parts are the even/odd elements of the original real data), followed by O(N) post-processing operations.
It was once believed that real-input DFTs could be more efficiently computed by means of the discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs. Bruun's algorithm (above) is another method that was initially proposed to take advantage of real inputs, but it has not proved popular.
There are further FFT specializations for the cases of real data that have even/odd symmetry, in which case one can gain another factor of roughly two in time and memory and the DFT becomes the discrete cosine/sine transform(s) (DCT/DST). Instead of directly modifying an FFT algorithm for these cases, DCTs/DSTs can also be computed via FFTs of real data combined with O(N) pre- and post-processing.
What is the Discrete Cosine Transform?
A discrete cosine transform ( DCT ) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT , first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC ), digital television (such as SDTV, HDTV and VOD ), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
The most common variant of discrete cosine transform is the type-II DCT , which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT , is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs ( MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT . A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT . One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT ,: ix, xiii, 1, 141–304 used in several ISO /IEC and ITU-T international standards.
What is the Discrete Sine Transform?
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample.
A family of transforms composed of sine and sine hyperbolic functions exists. These transforms are made based on the natural vibration of thin square plates with different boundary conditions.
The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed T. Natarajan and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978.
Notable settings
windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm
SS = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods
Fmin1 = zeroes out frequencies not passing this test for min value
Fmax1 = zeroes out frequencies not passing this test for max value
barsback = moves the window backward
Inverse = whether or not you wish to invert the FFT after first pass calculation
Related indicators
Real-Fast Fourier Transform of Price Oscillator
STD-Stepped Fast Cosine Transform Moving Average
Real-Fast Fourier Transform of Price w/ Linear Regression
Variety RSI of Fast Discrete Cosine Transform
Additional reading
A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al.
Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al.
Cooley–Tukey FFT algorithm
Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. doi:10.1016/1051-2004(91)90086-Z.
DCT-History - How I Came Up With The Discrete Cosine Transform
Comparative Analysis for Discrete Sine Transform as a suitable method for noise estimation
Helme-Nikias Weighted Burg AR-SE Extra. of Price [Loxx]Helme-Nikias Weighted Burg AR-SE Extra. of Price is an indicator that uses an autoregressive spectral estimation called the Weighted Burg Algorithm, but unlike the usual WB algo, this one uses Helme-Nikias weighting. This method is commonly used in speech modeling and speech prediction engines. This is a linear method of forecasting data. You'll notice that this method uses a different weighting calculation vs Weighted Burg method. This new weighting is the following:
w = math.pow(array.get(x, i - 1), 2), the squared lag of the source parameter
and
w += math.pow(array.get(x, i), 2), the sum of the squared source parameter
This take place of the rectangular, hamming and parabolic weighting used in the Weighted Burg method
Also, this method includes Levinson–Durbin algorithm. as was already discussed previously in the following indicator:
Levinson-Durbin Autocorrelation Extrapolation of Price
What is Helme-Nikias Weighted Burg Autoregressive Spectral Estimate Extrapolation of price?
In this paper a new stable modification of the weighted Burg technique for autoregressive (AR) spectral estimation is introduced based on data-adaptive weights that are proportional to the common power of the forward and backward AR process realizations. It is shown that AR spectra of short length sinusoidal signals generated by the new approach do not exhibit phase dependence or line-splitting. Further, it is demonstrated that improvements in resolution may be so obtained relative to other weighted Burg algorithms. The method suggested here is shown to resolve two closely-spaced peaks of dynamic range 24 dB whereas the modified Burg schemes employing rectangular, Hamming or "optimum" parabolic windows fail.
Data inputs
Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar
LastBar - bar where to start the prediction
PastBars - how many bars back to model
LPOrder - order of linear prediction model; 0 to 1
FutBars - how many bars you want to forward predict
Things to know
Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages.
This indicator repaints
Further reading
A high-resolution modified Burg algorithm for spectral estimation
Related Indicators
Levinson-Durbin Autocorrelation Extrapolation of Price
Weighted Burg AR Spectral Estimate Extrapolation of Price
vol_boxA simple script to draw a realized volatility forecast, in the form of a box. The script calculates realized volatility using the EWMA method, using a number of periods of your choosing. Using the "periods per year", you can adjust the script to work on any time frame. For example, if you are using an hourly chart with bitcoin, there are 24 periods * 365 = 8760 periods per year. This setting is essential for the realized volatility figure to be accurate as an annualized figure, like VIX.
By default, the settings are set to mimic CBOE volatility indices. That is, 252 days per year, and 20 period window on the daily timeframe (simulating a 30 trading day period).
Inside the box are three figures:
1. The current realized volatility.
2. The rank. E.g. "10%" means the current realized volatility is less than 90% of realized volatility measures.
3. The "accuracy": how often price has closed within the box, historically.
Inputs:
stdevs: the number of standard deviations for the box
periods to project: the number of periods to forecast
window: the number of periods for calculating realized volatility
periods per year: the number of periods in one year (e.g. 252 for the "D" timeframe)
FOMC AnnouncementsThis indicator plots vertical lines at the scheduled times of US Federal Reserve's FOMC Meeting Announcements. Usually, that time or the 24 hours before and after could see big moves in markets. You can change those dates and times in the settings, and could use the indicator option "Add this indicator to entire layout" if you want to easily reflect that across all panes of a layout. Those lines will show on any symbol you switch to, saving you time and effort of drawing them manually.
