vol_rangesThis script shows three measures of volatility:
historical (hv): realized volatility of the recent past
median (mv): a long run average of realized volatility
implied (iv): a user-defined volatility
Historical and median volatility are based on the EWMA, rather than standard deviation, method of calculating volatility. Since Tradingview's built in ema function uses a window, the "window" parameter determines how much historical data is used to calculate these volatility measures. E.g. 30 on a daily chart means the previous 30 days.
The plots above and below historical candles show past projections based on these measures. The "periods to expiration" dictates how far the projection extends. At 30 periods to expiration (default), the plot will indicate the one standard deviation range from 30 periods ago. This is calculated by multiplying the volatility measure by the square root of time. For example, if the historical volatility (hv) was 20% and the window is 30, then the plot is drawn over: close * 1.2 * sqrt(30/252).
At the most recent candle, this same calculation is simply drawn as a line projecting into the future.
This script is intended to be used with a particular options contract in mind. For example, if the option expires in 15 days and has an implied volatility of 25%, choose 15 for the window and 25 for the implied volatility options. The ranges drawn will reflect the two standard deviation range both in the future (lines) and at any point in the past (plots) for HV (blue), MV (red), and IV (grey).
Cerca negli script per "Implied volatility"
Implied and Historical VolatilityAbstract
This TradingView indicator visualizes implied volatility (IV) derived from the VIX index and historical volatility (HV) computed from past price data of the S&P 500 (or any selected asset). It enables users to compare market participants' forward-looking volatility expectations (via VIX) with realized past volatility (via historical returns). Such comparisons are pivotal in identifying risk sentiment, volatility regimes, and potential mispricing in derivatives.
Functionality
Implied Volatility (IV):
The implied volatility is extracted from the VIX index, often referred to as the "fear gauge." The VIX represents the market's expectation of 30-day forward volatility, derived from options pricing on the S&P 500. Higher values of VIX indicate increased uncertainty and risk aversion (Whaley, 2000).
Historical Volatility (HV):
The historical volatility is calculated using the standard deviation of logarithmic returns over a user-defined period (default: 20 trading days). The result is annualized using a scaling factor (default: 252 trading days). Historical volatility represents the asset's past price fluctuation intensity, often used as a benchmark for realized risk (Hull, 2018).
Dynamic Background Visualization:
A dynamic background is used to highlight the relationship between IV and HV:
Yellow background: Implied volatility exceeds historical volatility, signaling elevated market expectations relative to past realized risk.
Blue background: Historical volatility exceeds implied volatility, suggesting the market might be underestimating future uncertainty.
Use Cases
Options Pricing and Trading:
The disparity between IV and HV provides insights into whether options are over- or underpriced. For example, when IV is significantly higher than HV, options traders might consider selling volatility-based derivatives to capitalize on elevated premiums (Natenberg, 1994).
Market Sentiment Analysis:
Implied volatility is often used as a proxy for market sentiment. Comparing IV to HV can help identify whether the market is overly optimistic or pessimistic about future risks.
Risk Management:
Institutional and retail investors alike use volatility measures to adjust portfolio risk exposure. Periods of high implied or historical volatility might necessitate rebalancing strategies to mitigate potential drawdowns (Campbell et al., 2001).
Volatility Trading Strategies:
Traders employing volatility arbitrage can benefit from understanding the IV/HV relationship. Strategies such as "long gamma" positions (buying options when IV < HV) or "short gamma" (selling options when IV > HV) are directly informed by these metrics.
Scientific Basis
The indicator leverages established financial principles:
Implied Volatility: Derived from the Black-Scholes-Merton model, implied volatility reflects the market's aggregate expectation of future price fluctuations (Black & Scholes, 1973).
Historical Volatility: Computed as the realized standard deviation of asset returns, historical volatility measures the intensity of past price movements, forming the basis for risk quantification (Jorion, 2007).
Behavioral Implications: IV often deviates from HV due to behavioral biases such as risk aversion and herding, creating opportunities for arbitrage (Baker & Wurgler, 2007).
Practical Considerations
Input Flexibility: Users can modify the length of the HV calculation and the annualization factor to suit specific markets or instruments.
Market Selection: The default ticker for implied volatility is the VIX (CBOE:VIX), but other volatility indices can be substituted for assets outside the S&P 500.
Data Frequency: This indicator is most effective on daily charts, as VIX data typically updates at a daily frequency.
Limitations
Implied volatility reflects the market's consensus but does not guarantee future accuracy, as it is subject to rapid adjustments based on news or events.
Historical volatility assumes a stationary distribution of returns, which might not hold during structural breaks or crises (Engle, 1982).
References
Black, F., & Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81(3), 637-654.
Whaley, R. E. (2000). "The Investor Fear Gauge." The Journal of Portfolio Management, 26(3), 12-17.
Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson Education.
Natenberg, S. (1994). Option Volatility and Pricing: Advanced Trading Strategies and Techniques. McGraw-Hill.
Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (2001). The Econometrics of Financial Markets. Princeton University Press.
Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill.
Baker, M., & Wurgler, J. (2007). "Investor Sentiment in the Stock Market." Journal of Economic Perspectives, 21(2), 129-151.
Williams Vix Fix ultra complete indicator (Tartigradia)Williams VixFix is a realized volatility indicator developed by Larry Williams, and can help in finding market bottoms.
Indeed, as Williams describe in his paper, markets tend to find the lowest prices during times of highest volatility, which usually accompany times of highest fear. The VixFix is calculated as how much the current low price statistically deviates from the maximum within a given look-back period.
Although the VixFix originally only indicates market bottoms, its inverse may indicate market tops. As masa_crypto writes : "The inverse can be formulated by considering "how much the current high value statistically deviates from the minimum within a given look-back period." This transformation equates Vix_Fix_inverse. This indicator can be used for finding market tops, and therefore, is a good signal for a timing for taking a short position." However, in practice, the Inverse VixFix is much less reliable than the classical VixFix, but is nevertheless a good addition to get some additional context.
For more information on the Vix Fix, which is a strategy published under public domain:
* The VIX Fix, Larry Williams, Active Trader magazine, December 2007, web.archive.org
* Fixing the VIX: An Indicator to Beat Fear, Amber Hestla-Barnhart, Journal of Technical Analysis, March 13, 2015, ssrn.com
* Replicating the CBOE VIX using a synthetic volatility index trading algorithm, Dayne Cary and Gary van Vuuren, Cogent Economics & Finance, Volume 7, 2019, Issue 1, doi.org
Created By ChrisMoody on 12-26-2014...
V3 MAJOR Update on 1-05-2014
tista merged LazyBear's Black Dots filter in 2020:
Extended by Tartigradia in 10-2022:
* Can select a symbol different from current to calculate vixfix, allows to select SP:SPX to mimic the original VIX index.
* Inverse VixFix (from masa_crypto and web.archive.org)
* VixFix OHLC Bars plot
* Price / VixFix Candles plot (Pro Tip: draw trend lines to find good entry/exit points)
* Add ADX filtering, Minimaxis signals, Minimaxis filtering (from samgozman )
* Convert to pinescript v5
* Allow timeframe selection (MTF)
* Skip off days (more accurate reproduction of original VIX)
* Reorganized, cleaned up code, commented out parts, commented out or removed unused code (eg, some of the KC calculations)
* Changed default Bollinger Band settings to reduce false positives in crypto markets.
Set Index symbol to SPX, and index_current = false, and timeframe Weekly, to reproduce the original VIX as close as possible by the VIXFIX (use the Add Symbol option, because you want to plot CBOE:VIX on the same timeframe as the current chart, which may include extended session / weekends). With the Weekly timeframe, off days / extended session days should not change much, but with lower timeframes this is important, because nights and weekends can change how the graph appears and seemingly make them different because of timing misalignment when in reality they are not when properly aligned.
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks [Loxx]Black-Scholes 1973 OPM on Non-Dividend Paying Stocks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. Making b equal to r yields the BSM model where dividends are not considered. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. For our purposes here are, Analytical Greeks are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
**This version of the Black-Scholes formula can also be used to price American call options on a non-dividend-paying stock, since it will never be optimal to exercise the option before expiration.**
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Generalized Black-Scholes-Merton w/ Analytical Greeks [Loxx]Generalized Black-Scholes-Merton w/ Analytical Greeks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton (BSM) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega, DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Asay (1982) Margined Futures Option Pricing Model [Loxx]Asay (1982) Margined Futures Option Pricing Model is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures where premium is fully margined. This means the Risk-free Rate, dividend, and cost to carry are all zero. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model.
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model. <== this is the one used for this indicator!
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Black-76 Options on Futures [Loxx]Black-76 Options on Futures is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho futures option
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model. <== this is the one used for this indicator!
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model.
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Garman and Kohlhagen (1983) for Currency Options [Loxx]Garman and Kohlhagen (1983) for Currency Options is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version of BSMOPM is to price Currency Options. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP, Speed
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing for Currency Options
The Garman and Kohlhagen (1983) modified Black-Scholes model can be used to price European currency options; see also Grabbe (1983). The model is mathematically equivalent to the Merton (1973) model presented earlier. The only difference is that the dividend yield is replaced by the risk-free rate of the foreign currency rf:
c = S * e^(-rf * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^(-rf * T) * N(-d1)
where
d1 = (log(S / X) + (r - rf + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
For more information on currency options, see DeRosa (2000)
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
rf = Risk-free rate of the foreign currency
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Related indicators:
BSM OPM 1973 w/ Continuous Dividend Yield
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks
Generalized Black-Scholes-Merton w/ Analytical Greeks
Generalized Black-Scholes-Merton Option Pricing Formula
Sprenkle 1964 Option Pricing Model w/ Num. Greeks
Modified Bachelier Option Pricing Model w/ Num. Greeks
Bachelier 1900 Option Pricing Model w/ Numerical Greeks
BSM OPM 1973 w/ Continuous Dividend Yield [Loxx]Generalized Black-Scholes-Merton w/ Analytical Greeks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures, and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q. <== this is the one used for this indicator!
b = 0 ... gives the Black (1976) futures option model.
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model.
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
vol_coneDraws a volatility cone on the chart, using the contract's realized volatility (rv). The inputs are:
- window: the number of past periods to use for computing the realized volatility. VIX uses 30 calendar days, which is 21 trading days, so 21 is the default.
- stdevs: the number of standard deviations that the cone will cover.
- periods to project: the length of the volatility cone.
- periods per year: the number of periods in a year. for a daily chart, this is 252. for a thirty minute chart on a contract that trades 23 hours a day, this is 23 * 2 * 252 = 11592. for an accurate cone, this input must be set correctly, according to the chart's time frame.
- history: show the lagged projections. in other words, if the cone is set to project 21 periods in the future, the lines drawn show the top and bottom edges of the cone from 23 periods ago.
- rate: the current interest or discount rate. this is used to compute the forward price of the underlying contract. using an accurate forward price allows you to compare the realized volatility projection to the implied volatility projections derived from options prices.
Example settings for a 30 minute chart of a contract that trades 23 hours per day, with 1 standard deviation, a 21 day rv calculation, and half a day projected:
- stdevs: 1
- periods to project: 23
- window: 23 * 2 * 21 = 966
- periods per year: 23 * 2 * 252 = 11592
Additionally, a table is drawn in the upper right hand corner, with several values:
- rv: the contract's current realized volatility.
- rnk: the rv's percentile rank, compared to the rv values on past bars.
- acc: the proportion of times price settled inside, versus outside, the volatility cone, "periods to project" into the future. this should be around 65-70% for most contracts when the cone is set to 1 standard deviation.
- up: the upper bound of the cone for the projection period.
- dn: the lower bound of the cone for the projection period.
Limitations:
- pinescript only seems to be able to draw a limited distance into the future. If you choose too many "periods to project", the cone will start drawing vertically at some limit.
- the cone is not totally smooth owing to the facts a) it is comprised of a limited number of lines and b) each bar does not represent the same amount of time in pinescript, as some cross weekends, session gaps, etc.
Z-Score Normalized Volatility IndicesVolatility is one of the most important measures in financial markets, reflecting the extent of variation in asset prices over time. It is commonly viewed as a risk indicator, with higher volatility signifying greater uncertainty and potential for price swings, which can affect investment decisions. Understanding volatility and its dynamics is crucial for risk management and forecasting in both traditional and alternative asset classes.
Z-Score Normalization in Volatility Analysis
The Z-score is a statistical tool that quantifies how many standard deviations a given data point is from the mean of the dataset. It is calculated as:
Z = \frac{X - \mu}{\sigma}
Where X is the value of the data point, \mu is the mean of the dataset, and \sigma is the standard deviation of the dataset. In the context of volatility indices, the Z-score allows for the normalization of these values, enabling their comparison regardless of the original scale. This is particularly useful when analyzing volatility across multiple assets or asset classes.
This script utilizes the Z-score to normalize various volatility indices:
1. VIX (CBOE Volatility Index): A widely used indicator that measures the implied volatility of S&P 500 options. It is considered a barometer of market fear and uncertainty (Whaley, 2000).
2. VIX3M: Represents the 3-month implied volatility of the S&P 500 options, providing insight into medium-term volatility expectations.
3. VIX9D: The implied volatility for a 9-day S&P 500 options contract, which reflects short-term volatility expectations.
4. VVIX: The volatility of the VIX itself, which measures the uncertainty in the expectations of future volatility.
5. VXN: The Nasdaq-100 volatility index, representing implied volatility in the Nasdaq-100 options.
6. RVX: The Russell 2000 volatility index, tracking the implied volatility of options on the Russell 2000 Index.
7. VXD: Volatility for the Dow Jones Industrial Average.
8. MOVE: The implied volatility index for U.S. Treasury bonds, offering insight into expectations for interest rate volatility.
9. BVIX: Volatility of Bitcoin options, a useful indicator for understanding the risk in the cryptocurrency market.
10. GVZ: Volatility index for gold futures, reflecting the risk perception of gold prices.
11. OVX: Measures implied volatility for crude oil futures.
Volatility Clustering and Z-Score
The concept of volatility clustering—where high volatility tends to be followed by more high volatility—is well documented in financial literature. This phenomenon is fundamental in volatility modeling and highlights the persistence of periods of heightened market uncertainty (Bollerslev, 1986).
Moreover, studies by Andersen et al. (2012) explore how implied volatility indices, like the VIX, serve as predictors for future realized volatility, underlining the relationship between expected volatility and actual market behavior. The Z-score normalization process helps in making volatility data comparable across different asset classes, enabling more effective decision-making in volatility-based strategies.
Applications in Trading and Risk Management
By using Z-score normalization, traders can more easily assess deviations from the mean in volatility, helping to identify periods when volatility is unusually high or low. This can be used to adjust risk exposure or to implement volatility-based trading strategies, such as mean reversion strategies. Research suggests that volatility mean-reversion is a reliable pattern that can be exploited for profit (Christensen & Prabhala, 1998).
References:
• Andersen, T. G., Bollerslev, T., Diebold, F. X., & Vega, C. (2012). Realized volatility and correlation dynamics: A long-run approach. Journal of Financial Economics, 104(3), 385-406.
• Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
• Christensen, B. J., & Prabhala, N. R. (1998). The relation between implied and realized volatility. Journal of Financial Economics, 50(2), 125-150.
• Whaley, R. E. (2000). Derivatives on market volatility and the VIX index. Journal of Derivatives, 8(1), 71-84.
rv_iv_vrpThis script provides realized volatility (rv), implied volatility (iv), and volatility risk premium (vrp) information for each of CBOE's volatility indices. The individual outputs are:
- Blue/red line: the realized volatility. This is an annualized, 20-period moving average estimate of realized volatility--in other words, the variability in the instrument's actual returns. The line is blue when realized volatility is below implied volatility, red otherwise.
- Fuchsia line (opaque): the median of realized volatility. The median is based on all data between the "start" and "end" dates.
- Gray line (transparent): the implied volatility (iv). According to CBOE's volatility methodology, this is similar to a weighted average of out-of-the-money ivs for options with approximately 30 calendar days to expiration. Notice that we compare rv20 to iv30 because there are about twenty trading periods in thirty calendar days.
- Fuchsia line (transparent): the median of implied volatility.
- Lightly shaded gray background: the background between "start" and "end" is shaded a very light gray.
- Table: the table shows the current, percentile, and median values for iv, rv, and vrp. Percentile means the value is greater than "N" percent of all values for that measure.
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Volatility risk premium (vrp) is simply the difference between implied and realized volatility. Along with implied and realized volatility, traders interpret this measure in various ways. Some prefer to be buying options when there volatility, implied or realized, reaches absolute levels, or low risk premium, whereas others have the opposite opinion. However, all volatility traders like to look at these measures in relation to their past values, which this script assists with.
By the way, this script is similar to my "vol premia," which provides the vrp data for all of these instruments on one page. However, this script loads faster and lets you see historical data. I recommend viewing the indicator and the corresponding instrument at the same time, to see how volatility reacts to changes in the underlying price.
Dynamic Volatility Differential Model (DVDM)The Dynamic Volatility Differential Model (DVDM) is a quantitative trading strategy designed to exploit the spread between implied volatility (IV) and historical (realized) volatility (HV). This strategy identifies trading opportunities by dynamically adjusting thresholds based on the standard deviation of the volatility spread. The DVDM is versatile and applicable across various markets, including equity indices, commodities, and derivatives such as the FDAX (DAX Futures).
Key Components of the DVDM:
1. Implied Volatility (IV):
The IV is derived from options markets and reflects the market’s expectation of future price volatility. For instance, the strategy uses volatility indices such as the VIX (S&P 500), VXN (Nasdaq 100), or RVX (Russell 2000), depending on the target market. These indices serve as proxies for market sentiment and risk perception (Whaley, 2000).
2. Historical Volatility (HV):
The HV is computed from the log returns of the underlying asset’s price. It represents the actual volatility observed in the market over a defined lookback period, adjusted to annualized levels using a multiplier of \sqrt{252} for daily data (Hull, 2012).
3. Volatility Spread:
The difference between IV and HV forms the volatility spread, which is a measure of divergence between market expectations and actual market behavior.
4. Dynamic Thresholds:
Unlike static thresholds, the DVDM employs dynamic thresholds derived from the standard deviation of the volatility spread. The thresholds are scaled by a user-defined multiplier, ensuring adaptability to market conditions and volatility regimes (Christoffersen & Jacobs, 2004).
Trading Logic:
1. Long Entry:
A long position is initiated when the volatility spread exceeds the upper dynamic threshold, signaling that implied volatility is significantly higher than realized volatility. This condition suggests potential mean reversion, as markets may correct inflated risk premiums.
2. Short Entry:
A short position is initiated when the volatility spread falls below the lower dynamic threshold, indicating that implied volatility is significantly undervalued relative to realized volatility. This signals the possibility of increased market uncertainty.
3. Exit Conditions:
Positions are closed when the volatility spread crosses the zero line, signifying a normalization of the divergence.
Advantages of the DVDM:
1. Adaptability:
Dynamic thresholds allow the strategy to adjust to changing market conditions, making it suitable for both low-volatility and high-volatility environments.
2. Quantitative Precision:
The use of standard deviation-based thresholds enhances statistical reliability and reduces subjectivity in decision-making.
3. Market Versatility:
The strategy’s reliance on volatility metrics makes it universally applicable across asset classes and markets, ensuring robust performance.
Scientific Relevance:
The strategy builds on empirical research into the predictive power of implied volatility over realized volatility (Poon & Granger, 2003). By leveraging the divergence between these measures, the DVDM aligns with findings that IV often overestimates future volatility, creating opportunities for mean-reversion trades. Furthermore, the inclusion of dynamic thresholds aligns with risk management best practices by adapting to volatility clustering, a well-documented phenomenon in financial markets (Engle, 1982).
References:
1. Christoffersen, P., & Jacobs, K. (2004). The importance of the volatility risk premium for volatility forecasting. Journal of Financial and Quantitative Analysis, 39(2), 375-397.
2. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007.
3. Hull, J. C. (2012). Options, Futures, and Other Derivatives. Pearson Education.
4. Poon, S. H., & Granger, C. W. J. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, 41(2), 478-539.
5. Whaley, R. E. (2000). The investor fear gauge. Journal of Portfolio Management, 26(3), 12-17.
This strategy leverages quantitative techniques and statistical rigor to provide a systematic approach to volatility trading, making it a valuable tool for professional traders and quantitative analysts.
[blackcat] L1 Dynamic Volatility IndicatorThe volatility indicator (Volatility) is used to measure the magnitude and instability of price changes in financial markets or a specific asset. This thing is usually used to assess how risky the market is. The higher the volatility, the greater the fluctuation in asset prices, but brother, the risk is also relatively high! Here are some related terms and explanations:
- Historical Volatility: The actual volatility of asset prices over a certain period of time in the past. This thing is measured by calculating historical data.
- Implied Volatility: The volatility inferred from option market prices, used to measure market expectations for future price fluctuations.
- VIX Index (Volatility Index): Often referred to as the "fear index," it predicts the volatility of the US stock market within 30 days in advance. This is one of the most famous volatility indicators in global financial markets.
Volatility indicators are very important for investors and traders because they can help them understand how unstable and risky the market is, thereby making wiser investment decisions.
Today I want to introduce a volatility indicator that I have privately held for many years. It can use colors to judge sharp rises and falls! Of course, if you are smart enough, you can also predict some potential sharp rises and falls by looking at the trend!
In the financial field, volatility indicators measure the magnitude and instability of price changes in different assets. They are usually used to assess the level of market risk. The higher the volatility, the greater the fluctuation in asset prices and therefore higher risk. Historical Volatility refers to the actual volatility of asset prices over a certain period of time in the past, which can be measured by calculating historical data; while Implied Volatility is derived from option market prices and used to measure market expectations for future price fluctuations. In addition, VIX Index is commonly known as "fear index" and is used to predict volatility in the US stock market within 30 days. It is one of the most famous volatility indicators in global financial markets.
Volatility indicators are very important for investors and traders because they help them understand market uncertainty and risk, enabling them to make wiser investment decisions. The L1 Dynamic Volatility Indicator that I am introducing today is an indicator that measures volatility and can also judge sharp rises and falls through colors!
This indicator combines two technical indicators: Dynamic Volatility (DV) and ATR (Average True Range), displaying warnings about sharp rises or falls through color coding. DV has a slow but relatively smooth response, while ATR has a fast but more oscillating response. By utilizing their complementary characteristics, it is possible to construct a structure similar to MACD's fast-slow line structure. Of course, in order to achieve fast-slow lines for DV and ATR, first we need to unify their coordinate axes by normalizing them. Then whenever ATR's yellow line exceeds DV's purple line with both curves rapidly breaking through the threshold of 0.2, sharp rises or falls are imminent.
However, it is important to note that relying solely on the height and direction of these two lines is not enough to determine the direction of sharp rises or falls! Because they only judge the trend of volatility and cannot determine bull or bear markets! But it's okay, I have already considered this issue early on and added a magical gradient color band. When the color band gradually turns warm, it indicates a sharp rise; conversely, when the color band tends towards cool colors, it indicates a sharp fall! Of course, you won't see the color band in sideways consolidation areas, which avoids your involvement in unnecessary trades that would only waste your funds! This indicator is really practical and with it you can better assess market risks and opportunities!
Black-Scholes option price model & delta hedge strategyBlack-Scholes Option Pricing Model Strategy
The strategy is based on the Black-Scholes option pricing model and allows the calculation of option prices, various option metrics (the Greeks), and the creation of synthetic positions through delta hedging.
ATTENTION!
Trading derivative financial instruments involves high risks. The author of the strategy is not responsible for your financial results! The strategy is not self-sufficient for generating profit! It is created exclusively for constructing a synthetic derivative financial instrument. Also, there might be errors in the script, so use it at your own risk! I would appreciate it if you point out any mistakes in the comments! I would be even more grateful if you send the corrected code!
Application Scope
This strategy can be used for delta hedging short positions in sold options. For example, suppose you sold a call option on Bitcoin on the Deribit exchange with a strike price of $60,000 and an expiration date of September 27, 2024. Using this script, you can create a delta hedge to protect against the risk of loss in the option position if the price of Bitcoin rises.
Another example: Suppose you use staking of altcoins in your strategies, for which options are not available. By using this strategy, you can hedge the risk of a price drop (Put option). In this case, you won't lose money if the underlying asset price increases, unlike with a short futures position.
Another example: You received an airdrop, but your tokens will not be fully unlocked soon. Using this script, you can fully hedge your position and preserve their dollar value by the time the tokens are fully unlocked. And you won't fear the underlying asset price increasing, as the loss in the event of a price rise is limited to the option premium you will pay if you rebalance the portfolio.
Of course, this script can also be used for simple directional trading of momentum and mean reversion strategies!
Key Features and Input Parameters
1. Option settings:
- Style of option: "European vanilla", "Binary", "Asian geometric".
- Type of option: "Call" (bet on the rise) or "Put" (bet on the fall).
- Strike price: the option contract price.
- Expiration: the expiry date and time of the option contract.
2. Market statistic settings:
- Type of price source: open, high, low, close, hl2, hlc3, ohlc4, hlcc4 (using hl2, hlc3, ohlc4, hlcc4 allows smoothing the price in more volatile series).
- Risk-free return symbol: the risk-free rate for the market where the underlying asset is traded. For the cryptocurrency market, the return on the funding rate arbitrage strategy is accepted (a special function is written for its calculation based on the Premium Price).
- Volatility calculation model: realized (standard deviation over a moving period), implied (e.g., DVOL or VIX), or custom (you can specify a specific number in the field below). For the cryptocurrency market, the calculation of implied volatility is implemented based on the product of the realized volatility ratio of the considered asset and Bitcoin to the Bitcoin implied volatility index.
- User implied volatility: fixed implied volatility (used if "Custom" is selected in the "Volatility Calculation Method").
3. Display settings:
- Choose metric: what to display on the indicator scale – the price of the underlying asset, the option price, volatility, or Greeks (all are available).
- Measure: bps (basis points), percent. This parameter allows choosing the unit of measurement for the displayed metric (for all except the Greeks).
4. Trading settings:
- Hedge model: None (do not trade, default), Simple (just open a position for the full volume when the strike price is crossed), Synthetic option (creating a synthetic option based on the Black-Scholes model).
- Position side: Long, Short.
- Position size: the number of units of the underlying asset needed to create the option.
- Strategy start time: the moment in time after which the strategy will start working to create a synthetic option.
- Delta hedge interval: the interval in minutes for rebalancing the portfolio. For example, a value of 5 corresponds to rebalancing the portfolio every 5 minutes.
Post scriptum
My strategy based on the SegaRKO model. Many thanks to the author! Unfortunately, I don't have enough reputation points to include a link to the author in the description. You can find the original model via the link in the code, as well as through the search indicators on the charts by entering the name: "Black-Scholes Option Pricing Model". I have significantly improved the model: the calculation of volatility, risk-free rate and time value of the option have been reworked. The code performance has also been significantly optimized. And the most significant change is the execution, with which you can now trade using this script.
Prometheus Black-Scholes Option PricesThe Black-Scholes Model is an option pricing model developed my Fischer Black and Myron Scholes in 1973 at MIT. This is regarded as the most accurate pricing model and is still used today all over the world. This script is a simulated Black-Scholes model pricing model, I will get into why I say simulated.
What is an option?
An option is the right, but not the obligation, to buy or sell 100 shares of a certain stock, for calls or puts respective, at a certain price, on a certain date (assuming European style options, American options can be exercised early). The reason these agreements, these contracts exist is to provide traders with leverage. Buying 1 contract to represent 100 shares of the underlying, more often than not, at a cheaper price. That is why the price of the option, the premium , is a small number. If an option costs $1.00 we pay $100.00 for it because 100 shares * 1 dollar per share = 100 dollars for all the shares. When a trader purchases a call on stock XYZ with a strike of $105 while XYZ stock is trading at $100, if XYZ stock moves up to $110 dollars before expiration the option has $5 of intrinsic value. You have the right to buy something at $105 when it is trading at $110. That agreement is way more valuable now, as a result the options premium would increase. That is a quick overview about how options are traded, let's get into calculating them.
Inputs for the Black-Scholes model
To calculate the price of an option we need to know 5 things:
Current Price of the asset
Strike Price of the option
Time Till Expiration
Risk-Free Interest rate
Volatility
The price of a European call option 𝐶 is given by:
𝐶 = 𝑆0 * Φ(𝑑1) − 𝐾 * 𝑒^(−𝑟 * 𝑇) * Φ(𝑑2)
where:
𝑆0 is the current price of the underlying asset.
𝐾 is the strike price of the option.
𝑟 is the risk-free interest rate.
𝑇 is the time to expiration.
Φ is the cumulative distribution function of the standard normal distribution.
𝑑1 and 𝑑2 are calculated as:
𝑑1 = (ln(𝑆0 / 𝐾) + (𝑟 + (𝜎^2 / 2)) * 𝑇) / (𝜎 * sqrt(𝑇))
𝑑2= 𝑑1 - (𝜎 * sqrt(𝑇))
𝜎 is the volatility of the underlying asset.
The price of a European put option 𝑃 is given by:
𝑃 = 𝐾 * 𝑒^(−𝑟 * 𝑇) * Φ(−𝑑2) − 𝑆0 * Φ(−𝑑1)
where 𝑑1 and 𝑑2 are as defined above.
Key Assumptions of the Black-Scholes Model
The price of the underlying asset follows a lognormal distribution.
There are no transaction costs or taxes.
The risk-free interest rate and volatility of the underlying asset are constant.
The underlying asset does not pay dividends during the life of the option.
The markets are efficient, meaning that all known information is already reflected in the prices.
Options can only be exercised at expiration (European-style options).
Understanding the Script
Here I have arrows pointing to specific spots on the table. They point to Historical Volatility and Inputted DTE . Inputted DTE is a value the user may input to calculate premium for options that expire in that many days. Historical Volatility , is the value calculated by this code.
length = 252 // One year of trading days
hv = ta.stdev(math.log(close / close ), length) * math.sqrt(365)
And then made daily like the Black-Scholes model needs from this step in the code.
hv_daily = request.security(syminfo.tickerid, "1D", hv)
The user has the option to input their own volatility to the Script. I will get into why that may be advantageous in a moment. If the user chooses to do so the Script will change which value it is using as so.
hv_in_use = which_sig == false ? hv_daily : sig
There is a lot going on in this image but bare with me, it will all make sense by the end. The column to the far left of both the green and maroon colored columns represent the strike price of the contract, if the numbers are white that means the contract is out of the money, gray means in the money. If you remember from the calculation this represents the price to buy or sell shares at, for calls or puts respective. The column second from the left shows a value for Simulated Market Price . This is a necessary part of this script so we can show changes in implied volatility. See, when we go to our brokerages and look at options prices, sure the price was calculated by a pricing model, but that is rarely the true price of the model. Market participant sentiment affects this value as their estimates for future volatility, Implied Volatility changes.
For example, if a call option is supposed to be worth $1.00 from the pricing model, however everyone is bullish on the stock and wants to buy calls, the premium may go to $1.20 from $1.00 because participants juice up the Implied Volatility . Higher Implied Volatility generally means higher premium, given enough time to expiration. Buying an option at $0.80 when it should be worth $1.00 due to changes in sentiment is a big part of the Quant Trading industry.
Of course I don't have access to an actual exchange so get prices, so I modeled participant decisions by adding or subtracting a small random value on the "perfect premium" from the Black-Scholes model, and solving for implied volatility using the Newton-Raphson method.
It is like when we have speed = distance / time if we know speed and time , we can solve for distance .
This is what models the changing Implied Volatility in the table. The other column in the table, 3rd from the left, is the Black-Scholes model price without the changes of a random number. Finally, the 4th column from the left is that Implied Volatility value we calculated with the modified option price.
More on Implied Volatility
Implied Volatility represents the future expected volatility of an asset. As it is the value in the future it is not know like Historical Volatility, only projected. We provide the user with the option to enter their own Implied Volatility to start with for better modeling of options close to expiration. If you want to model options 1 day from expiration you will probably have to enter a higher Implied Volatility so that way the prices will be higher. Since the underlying is so close to expiration they are traded so much and traders manipulate their Implied Volatility , increasing their value. Be safe while trading these!
Thank you all for clicking on my indicator and reading this description! Happy coding, Happy trading, Be safe!
Good reference: www.investopedia.com
VOLQ Sigma TableThis indicator replaces the implied volatility of VOLQ with the daily volatility and reflects that value into the price on the NDX chart to create the VOLQ standard deviation table.
It will only be useful for stocks related to the Nasdaq Index.
For example, NDX, QQQ or so.
And we want to predict the range of weekly fluctuations by plotting those values as a line in the future.
It is expressed as High 2σ by adding the standard deviation 2 sigma value of the VOLQ value from last week's closing price.
It is expressed as High 1σ by adding the standard deviation 1 sigma value of the VOLQ value from last week's closing price.
It is expressed as Low 1σ by subtracting the standard deviation 1 sigma value of the VOLQ value from the closing price of the previous week.
It is expressed as Low 2σ by subtracting the standard deviation 2 sigma value of the VOLQ value from last week's closing price.
1day predicts daily fluctuations.
2day predicts 2-day fluctuations.
3day predicts 3-day fluctuations.
4day predicts 4-day fluctuations.
5day predicts 5-day fluctuations.
In the settings you can select the start date to display the VOLQ line via input.
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What motivated me to create this indicator?
From my point of view, the reason for classifying vix volq historical volatility (realized volatility) is that the most important point is that VIXX and VolQ are calculated from implied volatility. It can be standardized as one-month volatility. There are many strike prices, but exchanges use the implied volatility of options traded on their own exchanges.
Because historical volatility depends on how the period is set, to compare with VIXX, we compare it with a month, that is, 20 business days. One-month implied volatility means (actually different depending on the strike price), because option traders expect that the one-month volatility will be this much, and it is the volatility created by volatility trading.
So we see it as the volatility expected by derivatives traders, especially volatility traders.
I'm trying to infer what the market thinks will fluctuate this much from the numbers generated there.
IV Rank and Percentile"All stocks in the market have unique personalities in terms of implied volatility (their option prices). For example, one stock might have an implied volatility of 30%, while another has an implied volatility of 50%. Even more, the 30% IV stock might usually trade with 20% IV, in which case 30% is high. On the other hand, the 50% IV stock might usually trade with 75% IV, in which case 50% is low.
So, how do we determine whether a stock's option prices (IV) are relatively high or low?
The solution is to compare each stock's IV against its historical IV levels. We can accomplish this by converting a stock's current IV into a rank or percentile.
Implied Volatility Rank (IV Rank) Explained
Implied volatility rank (IV rank) compares a stock's current IV to its IV range over a certain time period (typically one year).
Here's the formula for one-year IV rank:
(Current IV - 1 Year Low IV) / (1 Year High IV - 1 Year Low IV) * 100
For example, the IV rank for a 20% IV stock with a one-year IV range between 15% and 35% would be:
(20% - 15%) / (35% - 15%) = 25%
An IV rank of 25% means that the difference between the current IV and the low IV is only 25% of the entire IV range over the past year, which means the current IV is closer to the low end of historical levels of implied volatility.
Furthermore, an IV rank of 0% indicates that the current IV is the very bottom of the one-year range, and an IV rank of 100% indicates that the current IV is at the top of the one-year range.
Implied Volatility Percentile (IV Percentile) Explained
Implied volatility percentile (IV percentile) tells you the percentage of days in the past that a stock's IV was lower than its current IV.
Here's the formula for calculating a one-year IV percentile:
Number of trading days below current IV / 252 * 100
As an example, let's say a stock's current IV is 35%, and in 180 of the past 252 days, the stock's IV has been below 35%. In this case, the stock's 35% implied volatility represents an IV percentile equal to:
180/252 * 100 = 71.42%
An IV percentile of 71.42% tells us that the stock's IV has been below 35% approximately 71% of the time over the past year.
Applications of IV Rank and IV Percentile
Why does it help to know whether a stock's current implied volatility is relatively high or low? Well, many traders use IV rank or IV percentile as a way to determine appropriate strategies for that stock.
For example, if a stock's IV rank is 90%, then a trader might look to implement strategies that profit from a decrease in the stock's implied volatility, as the IV rank of 90% indicates that the stock's current IV is at the top of its range over the past year (for a one-year IV rank).
On the other hand, if a stock's IV rank is 0%, then traders might look to implement strategies that profit from an increase in implied volatility, as the IV rank of 0% indicates the stock's current implied volatility is at the bottom of its range over the past year."
This script approximates IV by using the VIX products, which calculate the 30-day implied volatility of the specified security.
*Includes an option for repainting -- default value is true, meaning the script will repaint the current bar.
False = Not Repainting = Value for the current bar is not repainted, but all past values are offset by 1 bar.
True = Repainting = Value for the current bar is repainted, but all past values are correct and not offset by 1 bar.
In both cases, all of the historical values are correct, it is just a matter of whether you prefer the current bar to be realistically painted and the historical bars offset by 1, or the current bar to be repainted and the historical data to match their respective price bars.
As explained by TradingView,`f_security()` is for coders who want to offer their users a repainting/no-repainting version of the HTF data.
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
Rule of 16 - LowerThe "Rule of 16" is a simple guideline used by traders and investors to estimate the expected annualized volatility of the S&P 500 Index (SPX) based on the level of the CBOE Volatility Index (VIX). The VIX, often referred to as the "fear gauge" or "fear index," measures the market's expectations for future volatility. It is calculated using the implied volatility of a specific set of S&P 500 options.
The Rule of 16 provides a rough approximation of the expected annualized percentage change in the S&P 500 based on the VIX level. Here's how it works:
Find the VIX level: Look up the current value of the VIX. Let's say it's currently at 20.
Apply the Rule of 16: Divide the VIX level by 16. In this example, 20 divided by 16 equals 1.25.
Result: The result of this calculation represents the expected annualized percentage change in the S&P 500. In this case, 1.25% is the estimated annualized volatility.
So, according to the Rule of 16, a VIX level of 20 suggests an expected annualized volatility of approximately 1.25% in the S&P 500.
Here's how you can use the Rule of 16:
Market Sentiment: The VIX is often used as an indicator of market sentiment. When the VIX is high (above its historical average), it suggests that investors expect higher market volatility, indicating potential uncertainty or fear in the markets. Conversely, when the VIX is low, it suggests lower expected volatility and potentially more confidence in the markets.
Risk Management: Traders and investors can use the Rule of 16 to estimate the potential risk associated with their portfolios. For example, if you have a portfolio of S&P 500 stocks and the VIX is at 20, you can use the Rule of 16 to estimate that the annualized volatility of your portfolio may be around 1.25%. This information can help you make decisions about position sizing and risk management.
Option Pricing: Options traders may use the Rule of 16 to get a quick estimate of the implied annualized volatility priced into S&P 500 options. It can help them assess whether options are relatively expensive or cheap based on the VIX level.
It's important to note that the Rule of 16 is a simplification and provides only a rough estimate of expected volatility. Market conditions and the relationship between the VIX and the S&P 500 can change over time. Therefore, it should be used as a guideline rather than a precise forecasting tool. Traders and investors should consider other factors and use additional analysis to make informed decisions.
Implied and Historical Volatility v4There is a famous option strategy📊 played on volatility📈. Where people go short on volatility, generally, this strategy is used before any significant event or earnings release. The basic phenomenon is that the Implied Volatility shoots up before the event and drops after the event, while the volatility of the security does not increase in most of the scenarios. 💹
I have tried to create an Indicator using which you
can analyse the historical change in Implied Volatility Vs Historic Volatility.
To get a basic idea of how the security moved during different events.
Notes:
a) Implied Volatility is calculated using the bisection method and Black 76 model option pricing model.
b) For the risk-free rate I have fetched the price of the “10-Year Indian Government Bond” price and calculated its yield to be used as our Risk-Free rate.
Z-Score Normalized VIX StrategyThis strategy leverages the concept of the Z-score applied to multiple VIX-based volatility indices, specifically designed to capture market reversals based on the normalization of volatility. The strategy takes advantage of VIX-related indicators to measure extreme levels of market fear or greed and adjusts its position accordingly.
1. Overview of the Z-Score Methodology
The Z-score is a statistical measure that describes the position of a value relative to the mean of a distribution in terms of standard deviations. In this strategy, the Z-score is calculated for various volatility indices to assess how far their values are from their historical averages, thus normalizing volatility levels. The Z-score is calculated as follows:
Z = \frac{X - \mu}{\sigma}
Where:
• X is the current value of the volatility index.
• \mu is the mean of the index over a specified period.
• \sigma is the standard deviation of the index over the same period.
This measure tells us how many standard deviations the current value of the index is away from its average, indicating whether the market is experiencing unusually high or low volatility (fear or calm).
2. VIX Indices Used in the Strategy
The strategy utilizes four commonly referenced volatility indices:
• VIX (CBOE Volatility Index): Measures the market’s expectations of 30-day volatility based on S&P 500 options.
• VIX3M (3-Month VIX): Reflects expectations of volatility over the next three months.
• VIX9D (9-Day VIX): Reflects shorter-term volatility expectations.
• VVIX (VIX of VIX): Measures the volatility of the VIX itself, indicating the level of uncertainty in the volatility index.
These indices provide a comprehensive view of the current volatility landscape across different time horizons.
3. Strategy Logic
The strategy follows a long entry condition and an exit condition based on the combined Z-score of the selected volatility indices:
• Long Entry Condition: The strategy enters a long position when the combined Z-score of the selected VIX indices falls below a user-defined threshold, indicating an abnormally low level of volatility (suggesting a potential market bottom and a bullish reversal). The threshold is set as a negative value (e.g., -1), where a more negative Z-score implies greater deviation below the mean.
• Exit Condition: The strategy exits the long position when the combined Z-score exceeds the threshold (i.e., when the market volatility increases above the threshold, indicating a shift in market sentiment and reduced likelihood of continued upward momentum).
4. User Inputs
• Z-Score Lookback Period: The user can adjust the lookback period for calculating the Z-score (e.g., 6 periods).
• Z-Score Threshold: A customizable threshold value to define when the market has reached an extreme volatility level, triggering entries and exits.
The strategy also allows users to select which VIX indices to use, with checkboxes to enable or disable each index in the calculation of the combined Z-score.
5. Trade Execution Parameters
• Initial Capital: The strategy assumes an initial capital of $20,000.
• Pyramiding: The strategy does not allow pyramiding (multiple positions in the same direction).
• Commission and Slippage: The commission is set at $0.05 per contract, and slippage is set at 1 tick.
6. Statistical Basis of the Z-Score Approach
The Z-score methodology is a standard technique in statistics and finance, commonly used in risk management and for identifying outliers or unusual events. According to Dumas, Fleming, and Whaley (1998), volatility indices like the VIX serve as a useful proxy for market sentiment, particularly during periods of high uncertainty. By calculating the Z-score, we normalize volatility and quantify the degree to which the current volatility deviates from historical norms, allowing for systematic entry and exit based on these deviations.
7. Implications of the Strategy
This strategy aims to exploit market conditions where volatility has deviated significantly from its historical mean. When the Z-score falls below the threshold, it suggests that the market has become excessively calm, potentially indicating an overreaction to past market events. Entering long positions under such conditions could capture market reversals as fear subsides and volatility normalizes. Conversely, when the Z-score rises above the threshold, it signals increased volatility, which could be indicative of a bearish shift in the market, prompting an exit from the position.
By applying this Z-score normalized approach, the strategy seeks to achieve more consistent entry and exit points by reducing reliance on subjective interpretation of market conditions.
8. Scientific Sources
• Dumas, B., Fleming, J., & Whaley, R. (1998). “Implied Volatility Functions: Empirical Tests”. The Journal of Finance, 53(6), 2059-2106. This paper discusses the use of volatility indices and their empirical behavior, providing context for volatility-based strategies.
• Black, F., & Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities”. Journal of Political Economy, 81(3), 637-654. The original Black-Scholes model, which forms the basis for many volatility-related strategies.
Volatility IndicatorThe volatility indicator presented here is based on multiple volatility indices that reflect the market’s expectation of future price fluctuations across different asset classes, including equities, commodities, and currencies. These indices serve as valuable tools for traders and analysts seeking to anticipate potential market movements, as volatility is a key factor influencing asset prices and market dynamics (Bollerslev, 1986).
Volatility, defined as the magnitude of price changes, is often regarded as a measure of market uncertainty or risk. Financial markets exhibit periods of heightened volatility that may precede significant price movements, whether upward or downward (Christoffersen, 1998). The indicator presented in this script tracks several key volatility indices, including the VIX (S&P 500), GVZ (Gold), OVX (Crude Oil), and others, to help identify periods of increased uncertainty that could signal potential market turning points.
Volatility Indices and Their Relevance
Volatility indices like the VIX are considered “fear gauges” as they reflect the market’s expectation of future volatility derived from the pricing of options. A rising VIX typically signals increasing investor uncertainty and fear, which often precedes market corrections or significant price movements. In contrast, a falling VIX may suggest complacency or confidence in continued market stability (Whaley, 2000).
The other volatility indices incorporated in the indicator script, such as the GVZ (Gold Volatility Index) and OVX (Oil Volatility Index), capture the market’s perception of volatility in specific asset classes. For instance, GVZ reflects market expectations for volatility in the gold market, which can be influenced by factors such as geopolitical instability, inflation expectations, and changes in investor sentiment toward safe-haven assets. Similarly, OVX tracks the implied volatility of crude oil options, which is a crucial factor for predicting price movements in energy markets, often driven by geopolitical events, OPEC decisions, and supply-demand imbalances (Pindyck, 2004).
Using the Indicator to Identify Market Movements
The volatility indicator alerts traders when specific volatility indices exceed a defined threshold, which may signal a change in market sentiment or an upcoming price movement. These thresholds, set by the user, are typically based on historical levels of volatility that have preceded significant market changes. When a volatility index exceeds this threshold, it suggests that market participants expect greater uncertainty, which often correlates with increased price volatility and the possibility of a trend reversal.
For example, if the VIX exceeds a pre-determined level (e.g., 30), it could indicate that investors are anticipating heightened volatility in the equity markets, potentially signaling a downturn or correction in the broader market. On the other hand, if the OVX rises significantly, it could point to an upcoming sharp movement in crude oil prices, driven by changing market expectations about supply, demand, or geopolitical risks (Geman, 2005).
Practical Application
To effectively use this volatility indicator in market analysis, traders should monitor the alert signals generated when any of the volatility indices surpass their thresholds. This can be used to identify periods of market uncertainty or potential market turning points across different sectors, including equities, commodities, and currencies. The indicator can help traders prepare for increased price movements, adjust their risk management strategies, or even take advantage of anticipated price swings through options trading or volatility-based strategies (Black & Scholes, 1973).
Traders may also use this indicator in conjunction with other technical analysis tools to validate the potential for significant market movements. For example, if the VIX exceeds its threshold and the market is simultaneously approaching a critical technical support or resistance level, the trader might consider entering a position that capitalizes on the anticipated price breakout or reversal.
Conclusion
This volatility indicator is a robust tool for identifying market conditions that are conducive to significant price movements. By tracking the behavior of key volatility indices, traders can gain insights into the market’s expectations of future price fluctuations, enabling them to make more informed decisions regarding market entries and exits. Understanding and monitoring volatility can be particularly valuable during times of heightened uncertainty, as changes in volatility often precede substantial shifts in market direction (French et al., 1987).
References
• Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
• Christoffersen, P. F. (1998). Evaluating Interval Forecasts. International Economic Review, 39(4), 841-862.
• Whaley, R. E. (2000). Derivatives on Market Volatility. Journal of Derivatives, 7(4), 71-82.
• Pindyck, R. S. (2004). Volatility and the Pricing of Commodity Derivatives. Journal of Futures Markets, 24(11), 973-987.
• Geman, H. (2005). Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and Energy. John Wiley & Sons.
• Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
• French, K. R., Schwert, G. W., & Stambaugh, R. F. (1987). Expected Stock Returns and Volatility. Journal of Financial Economics, 19(1), 3-29.
