This indicator shows the expected range of movement of price given the assumption that price is log-normally distributed. This includes 3 multiples of standard deviation and 1 user selected level input as a multiple of standard deviation. Expected assumes that volatility remains static on the next bar. In reality, this may or may not be the case, so use caution when making broad assumptions about the levels shown when using this indicator. However, these levels match the same levels on Loxx's backtests and Multi-Panel indicator. These static levels are used as the take profit targets and stoploss on all Loxx's scripts previously posted.
This indicator can be be used on all timeframes, but the internal timeframe must be higher than the current timeframe or an error is thrown. The purpose for internal MTF is so that you can track the deviation range from higher timeframes on lower timeframes. When "current bar" is selected, this indicator will change with live prices changes. This is useful if you wish to enter a trade before the current bar closes and need to know the deviation ranges before the close. Current bar is also useful to see the past ranges of literally that bar. When "past bar" is selected, then the values shown on the current bar are values that were calculated on the last bar. The previous bar setting is useful to track price changes with the assumption that you entered a trade at the close of the previous bar. The default set to the previous bar. (careful, this default setting won't match Loxx's Muti-Panel tool since the Multi-Panel is built using the current bar. To make them match, you must change this setting to current bar)
I've included the ability for you to smooth the output around a moving average. Included are Loxx's Moving Averages. There are 41 to choose from. See more details here:
![Baseline Backtest [Loxx]](https://static.tradingview.com/static/images/svg/idea-image-placeholder.svg)
Smoothing applied yielding Keltner Channels
Also included are various UI options to manipulate line styling and colors.
Volatility Panel
Shows information about user selected volatility included confidence range of the chosen volatility. The following volatility types are included with additional volatility types to added in future releases.
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility .
Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.
Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility .
Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.
Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.
The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility .
One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility . That drawback is taken into account in the Garman-Klass's volatility estimator.
Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.
Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.
The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.
A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.
Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.
We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility ) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility . It considered being 14 times more efficient than the close-to-close estimator.
Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.
Standard Deviation of Log Returns
This is the simplest calculation of volatility . It's the standard deviation of ln(close/close(1))
Pseudo GARCH(2,2)
This is calculated using a short- and long-run mean of variance multiplied by θ.
θavg(var ;M) + (1 − θ) avg (var ;N) = 2θvar/(M+1-(M-1)L) + 2(1-θ)var/(M+1-(M-1)L)
Solving for θ can be done by minimizing the mean squared error of estimation; that is, regressing L^-1var - avg (var; N) against avg (var; M) - avg (var; N) and using the resulting beta estimate as θ.
Average True Range
The average true range (ATR) is a technical analysis indicator, introduced by market technician J. Welles Wilder Jr. in his book New Concepts in Technical Trading Systems, that measures market volatility by decomposing the entire range of an asset price for that period.
The true range indicator is taken as the greatest of the following: current high less the current low; the absolute value of the current high less the previous close; and the absolute value of the current low less the previous close. The ATR is then a moving average, generally using 14 days, of the true ranges.
True Range Double
A special case of ATR that attempts to correct for volatility skew.
Chi-squared Confidence Interval:
Confidence interval of volatility is calculated using an inverse CDF of a Chi-Squared Distribution. You can change the volatility input used to either realized, upper confidence interval, or lower confidence interval. This is included in case you'd like to see how far price can extend if volatility hits it's upper or lower confidence levels. Generally, you'd just used realized volatility , so I wouldn't change this setting.
Inverse CDF of a Chi-Squared Distribution
The chi-square distribution is a one-parameter family of curves. The parameter ν is the degrees of freedom.
The icdf of the chi-square distribution is
x=F^−1(p∣ν) = {x:F(x∣ν) = p}
where
p=F(x∣ν)= ∫ (t^(v-2)/2 * e^t/2) / (2^(v/2) / Γ(v/2))
ν is the degrees of freedom, and Γ( · ) is the Gamma function. The result p is the probability that a single observation from the chi-square distribution with ν degrees of freedom falls in the interval .
Related Indicators
Multi-Panel: Trade-Volatility-Probability
Variety Distribution Probability Cone
This indicator can be be used on all timeframes, but the internal timeframe must be higher than the current timeframe or an error is thrown. The purpose for internal MTF is so that you can track the deviation range from higher timeframes on lower timeframes. When "current bar" is selected, this indicator will change with live prices changes. This is useful if you wish to enter a trade before the current bar closes and need to know the deviation ranges before the close. Current bar is also useful to see the past ranges of literally that bar. When "past bar" is selected, then the values shown on the current bar are values that were calculated on the last bar. The previous bar setting is useful to track price changes with the assumption that you entered a trade at the close of the previous bar. The default set to the previous bar. (careful, this default setting won't match Loxx's Muti-Panel tool since the Multi-Panel is built using the current bar. To make them match, you must change this setting to current bar)
I've included the ability for you to smooth the output around a moving average. Included are Loxx's Moving Averages. There are 41 to choose from. See more details here:
![Baseline Backtest [Loxx]](https://s3.tradingview.com/0/0Jbdwapf_big.png)
Smoothing applied yielding Keltner Channels
Also included are various UI options to manipulate line styling and colors.
Volatility Panel
Shows information about user selected volatility included confidence range of the chosen volatility. The following volatility types are included with additional volatility types to added in future releases.
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility .
Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.
Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility .
Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.
Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.
The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility .
One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility . That drawback is taken into account in the Garman-Klass's volatility estimator.
Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.
Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.
The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.
A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.
Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.
We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility ) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility . It considered being 14 times more efficient than the close-to-close estimator.
Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.
Standard Deviation of Log Returns
This is the simplest calculation of volatility . It's the standard deviation of ln(close/close(1))
Pseudo GARCH(2,2)
This is calculated using a short- and long-run mean of variance multiplied by θ.
θavg(var ;M) + (1 − θ) avg (var ;N) = 2θvar/(M+1-(M-1)L) + 2(1-θ)var/(M+1-(M-1)L)
Solving for θ can be done by minimizing the mean squared error of estimation; that is, regressing L^-1var - avg (var; N) against avg (var; M) - avg (var; N) and using the resulting beta estimate as θ.
Average True Range
The average true range (ATR) is a technical analysis indicator, introduced by market technician J. Welles Wilder Jr. in his book New Concepts in Technical Trading Systems, that measures market volatility by decomposing the entire range of an asset price for that period.
The true range indicator is taken as the greatest of the following: current high less the current low; the absolute value of the current high less the previous close; and the absolute value of the current low less the previous close. The ATR is then a moving average, generally using 14 days, of the true ranges.
True Range Double
A special case of ATR that attempts to correct for volatility skew.
Chi-squared Confidence Interval:
Confidence interval of volatility is calculated using an inverse CDF of a Chi-Squared Distribution. You can change the volatility input used to either realized, upper confidence interval, or lower confidence interval. This is included in case you'd like to see how far price can extend if volatility hits it's upper or lower confidence levels. Generally, you'd just used realized volatility , so I wouldn't change this setting.
Inverse CDF of a Chi-Squared Distribution
The chi-square distribution is a one-parameter family of curves. The parameter ν is the degrees of freedom.
The icdf of the chi-square distribution is
x=F^−1(p∣ν) = {x:F(x∣ν) = p}
where
p=F(x∣ν)= ∫ (t^(v-2)/2 * e^t/2) / (2^(v/2) / Γ(v/2))
ν is the degrees of freedom, and Γ( · ) is the Gamma function. The result p is the probability that a single observation from the chi-square distribution with ν degrees of freedom falls in the interval .
Related Indicators
Multi-Panel: Trade-Volatility-Probability
![Multi-Panel: Trade-Volatility-Probability [Loxx]](https://s3.tradingview.com/s/SOo338Gf_big.png)
Variety Distribution Probability Cone
![Variety Distribution Probability Cone [Loxx]](https://s3.tradingview.com/0/0yeGVIBe_big.png)
Versionshinweise:
Small update to table values.
Public Telegram Group, t.me/algxtrading_public
VIP Membership Info: www.patreon.com/algxtrading/membership
VIP Membership Info: www.patreon.com/algxtrading/membership