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Impliedvolatility

Synthetic IV Rank [UAlgo]Synthetic IV Rank is a volatility analysis indicator that creates a practical proxy for IV Rank when direct options implied volatility data is not available. Instead of reading an options chain, the script estimates a synthetic volatility series from price action using a Yang Zhang style historical volatility model, then normalizes that value into a 0 to 100 rank across a user defined lookback window. This makes the tool especially useful for traders who want an IV Rank style workflow on instruments or markets where true implied volatility is unavailable, limited, or inconsistent. The indicator can be used on stocks, indices, forex, commodities, and crypto, with a dedicated Crypto Mode for annualization based on 365 days. The script is built as a separate pane indicator and focuses on clear regime awareness. It plots a smooth IV Rank line, adds visual threshold references for high and low volatility zones, and shows a live status label on the most recent bar with both the current rank and the raw synthetic volatility value. The overall design makes it suitable for fast regime checks, mean reversion context, premium selling style filters, and volatility expansion monitoring. Important note: This is a synthetic IV Rank approximation based on historical price volatility. It is not a substitute for true options implied volatility from an options chain. 🔹 Features 🔸 1) Synthetic IV Rank Using a Yang Zhang Style Volatility Model The indicator estimates volatility from price data using a Yang Zhang style framework, then converts that estimate into an IV Rank style percentile scale. This gives users an IV Rank like signal even when broker feeds do not provide options implied volatility. 🔸 2) Engine Based Design with Structured Inputs The script uses a custom VolatilityEngine type to organize the core calculation parameters: hv_length for volatility estimation length lookback_length for IV Rank normalization window annual_factor for market specific annualization This structure makes the logic easier to maintain and extend. 🔸 3) Stock and Crypto Annualization Modes The engine supports two annualization conventions through a simple input toggle: 252 day convention for traditional markets 365 day convention for crypto markets This is a practical detail because the same raw volatility process can produce different annualized values depending on the asset class. 🔸 4) Robust IV Rank Normalization with Safe Fallback The script computes IV Rank by comparing the current synthetic volatility value against the lowest and highest values over the selected lookback period. If the range collapses to zero, the script safely assigns a neutral rank of 50 instead of causing a division issue. This improves reliability in flat or low variance periods. 🔸 5) Clear Regime Visualization The indicator includes a strong visual layout designed for quick interpretation: A main IV Rank line A mid reference line at 50 High and low threshold markers at 80 and 20 Gradient fills that visually emphasize extreme zones This helps users recognize volatility regime shifts at a glance. 🔸 6) Dynamic Last Bar Status Labels On the latest bar, the script prints a compact status label that shows: Current IV Rank value Regime label such as EXTREME FEAR, COMPLACENCY, or NEUTRAL It also adds a secondary information label showing the raw Yang Zhang synthetic volatility percentage. This gives both normalized context and raw measurement at the same time. 🔸 7) Practical Regime Classification The script uses simple but effective thresholds for regime tagging: Above 80 signals elevated volatility conditions Below 20 signals compressed volatility conditions Between 20 and 80 is treated as neutral These thresholds align with common IV Rank style interpretation used in discretionary and systematic workflows. 🔹 Calculations 1) Engine Initialization On the first bar, the script initializes the custom volatility engine and stores: The Yang Zhang calculation length The IV Rank lookback window The annualization factor based on asset class mode If Crypto Mode is enabled, the annual factor uses the square root of 365. Otherwise it uses the square root of 252. 2) Synthetic Volatility Source Series The indicator computes a Yang Zhang style historical volatility estimate from OHLC data. The model combines multiple variance components so it can capture more market behavior than a simple close to close volatility series. The script calculates: A first variance component labeled as overnight in the comments An open to close variance component A Rogers Satchell style intraday variance component from high, low, open, and close relationships 3) First Variance Component (Commented as Overnight) In the current implementation, the first component is built from the logarithmic return of close / close , and its rolling variance is measured over the user defined length. This is important to note because the code comments describe an overnight style component, while the actual formula uses consecutive closes in the current version. 4) Open to Close Variance Component The script computes the logarithmic open to close return log(close / open) and then applies a rolling variance over the selected length. This measures intrabar movement relative to the bar open. 5) Rogers Satchell Intraday Variance Component To improve intraday variance estimation, the script calculates a Rogers Satchell style daily variance term using four logarithmic relationships derived from high, low, open, and close. It then smooths this with a rolling simple average across the same volatility length. This component is useful because it incorporates more intrabar range information than a simple close based measure. 6) Yang Zhang Weighting Factor The script computes a weighting coefficient k that depends on the volatility length. This weight balances the contribution of the open to close variance and the Rogers Satchell component in the final combined variance. The implementation follows the standard Yang Zhang style weighting formula shown in the script comments. 7) Combined Synthetic Volatility and Annualization After computing the variance components, the script combines them into a single Yang Zhang style variance estimate, takes the square root to obtain volatility, and annualizes the result with the engine annual factor. The final synthetic volatility value is expressed as a percentage. In practical terms, this output is the raw volatility series that the script later converts into Synthetic IV Rank. 8) IV Rank Calculation The IV Rank logic measures where the current synthetic volatility sits relative to its historical range over the selected lookback: It finds the lowest synthetic volatility in the lookback window It finds the highest synthetic volatility in the lookback window It scales the current value to a 0 to 100 rank If the lookback range is flat, the script assigns 50.0 as a neutral fallback. This normalization step is what makes the output behave like an IV Rank style regime indicator rather than a raw volatility plot. 9) Regime State Classification On the latest bar, the script assigns a text state from the current IV Rank: EXTREME FEAR when rank is above 80 COMPLACENCY when rank is below 20 NEUTRAL otherwise The label color also changes with the state, which improves visual scanning. 10) Visual Layer Logic The visualization includes: A plotted IV Rank line Hidden boundary plots for fill anchors Visible threshold markers at 80 and 20 A midpoint reference line at 50 Gradient fills for high volatility and low volatility zones The fill logic visually intensifies as the IV Rank moves deeper into an extreme zone, helping users identify volatility compression and expansion phases quickly. 11) What This Indicator Represents in Practice This script is best understood as a normalized historical volatility regime tool designed to mimic the workflow of IV Rank when direct implied volatility data is not available. It is excellent for context filtering and regime awareness, but it should not be interpreted as a true options market implied volatility feed.
Pine Script®指标
由UAlgo提供
Implied Volatility RangeThe Implied Volatility Range is a forward-looking tool that transforms option market data into probability ranges for future prices. Based on the lognormal distribution of asset prices assumed in modern option pricing models, it converts the implied volatility curve into a volatility cone with dynamic labels that show the market’s expectations for the price distribution at a specific point in time. At the selected future date, it displays projected price levels and their percentage change from today’s close across 1, 2, and 3 standard deviation (σ) ranges: 1σ range = ~68.2% probability the price will remain within this range. 2σ range = ~95.4% probability the price will remain within this range. 3σ range = ~99.7% probability the price will remain within this range. What makes this indicator especially useful is its ability to incorporate implied volatility skew. When only ATM IV (%) is entered, the indicator displays the standard Black–Scholes lognormal distribution. By adding High IV (%) and Low IV (%) values tied to strikes above and below the current price, the indicator interpolates between these inputs to approximate the implied volatility skew. This adjustment produces a market-implied probability distribution that indicates whether the option market is leaning bullish or bearish, based on the data entered in the menu: ATM IV (%) = Implied volatility at the current spot price (at-the-money). High IV (%) = Implied volatility at a strike above the current spot price. High Strike = Strike price corresponding to the High IV input (OTM call). Low IV (%) = Implied volatility at a strike below the current spot price. Low Strike = Strike price corresponding to the Low IV input (OTM put). Expiration (Day, Month, Year) = Option expiration date for the projection. Once these inputs are entered, the indicator calculates implied probability ranges and, if both High IV and Low IV values are provided, adjusts for skew to approximate the option market’s distribution. If no implied volatility data is supplied, the indicator defaults to a lognormal distribution based on historical volatility, using past realized volatility over the same forward horizon. This keeps the tool functional even without implied volatility inputs, though in that case the output represents only an approximation of ATM IV, not the actual market view. In summary, the Implied Volatility Range is a powerful tool that translates implied volatility inputs into a clear and practical estimate of the market’s expectations for future prices. It allows traders to visualize the probability of price ranges while also highlighting directional bias, a dimension often difficult to interpret from traditional implied volatility charts. It should be emphasized, however, that this tool reflects only the market’s expectations at a specific point in time, which may change as new information and trading activity reshape implied volatility.
Pine Script®指标
由QuantitativeAlpha提供
1
Synthetic VX3! & VX4! continuous /VX futuresTradingView is missing continuous 3rd and 4th month VIX (/VX) futures, so I decided to try to make a synthetic one that emulates what continuous maturity futures would look like. This is useful for backtesting/historical purposes as it enables traders to see how their further out VX contracts would've performed vs the front month contract. The indicator pulls actual realtime data (if you subscribe to the CBOE data package) or 15 minute delayed data for the VIX spot (the actual non-tradeable VIX index), the continuous front month (VX1!), and the continuous second month (VX2!) continually rolled contracts. Then the indicator's script applies a formula to fairly closely estimate how 3rd and 4th month continuous contracts would've moved. It uses an exponential mean‑reversion to a long‑run level formula using: σ(T) = θ+(σ0−θ)e−kT You can expect it to be off by ~5% or so (in times of backwardation it might be less accurate).
Pine Script®指标
由djayjp提供
2
Rectified BB% for option tradingThis indicator shows the bollinger bands against the price all expressed in percentage of the mean BB value. With one sight you can see the amplitude of BB and the variation of the price, evaluate a reenter of the price in the BB. The relative price is visualized as a candle with open/high/low/close value exspressed as percentage deviation from the BB mean The indicator include a modified RSI, remapped from 0/100 to -100/100. You can choose the BB parameters (length, standard deviation multiplier) and the RSI parameter (length, overbougth threshold, ovrsold threshold) You can exclude/include the candles and the RSI line. The indicator can be used to sell options when the volatility is high (the bollinger band is wide) and the price is reentering inside the bands. If the price is forming a supply or demand area it can be a good opportunity to sell a bull put or a bear call The RSI can be used as confirm of the supply/demand formation If the bollinger band is narrow and the RSI is overbought/oversold it indicate a better opportunity to buy options the indicator is designed to work with daily timeframe and default parameters.
Pine Script®指标
由Shagrath84提供
1
Implied Volatility Suite (TG Fork)Displays the Implied Volatility, which is usually calculated from options, but here is calculated indirectly from spot price directly, either using a model or model-free using the VIXfix. The model-free VIXfix based approach can detect times of high volatility, which usually coincides with panic and hence lowest prices. Inversely, the model-based approach can detect times of highest greed. Forked and updated by Tartigradia to fix some issues in the calculations, convert to pinescript v5 and reverse engineered to reproduce the "Implied Volatility Rank & Model Free IVR" indicator by the same author (but closed source) and allow to plot both model-based and model-free implied volatilities simultaneously. If you like this indicator, please show the original author SegaRKO some love:
Pine Script®指标
由tartigradia提供
4
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
Pine Script®指标
由loxx提供
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
Pine Script®指标
由loxx提供
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
Pine Script®指标
由loxx提供
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
Pine Script®指标
由loxx提供
1
Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]Generalized Black-Scholes-Merton Option Pricing Formula is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks aka "Option Sensitivities" and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". Black-Scholes-Merton Option Pricing The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize. It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them. Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion dS = mu * S * dt + v * S * dz where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process. The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that c = S * N(d1) - X * e^(-r * T) * N(d2) p = X * e^(-r * T) * N(d2) - S * N(d1) where d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5) d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5 Inputs S = Stock price. X = Strike price of option. T = Time to expiration in years. r = Risk-free rate b = Cost of carry v = Volatility of the underlying asset price cnd (x) = The cumulative normal distribution function nd(x) = The standard normal density function convertingToCCRate(r, cmp ) = Rate compounder gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm, float epsilon) = Implied volatility via Newton Raphson gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm) = implied volatility via bisection Implied Volatility: The Bisection Method The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility (vega) when searching for the implied volatility. For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values): 1. A "low" estimate of the implied volatility, al, corresponding to an option value, CL 2. A "high" volatility estimate, aH, corresponding to an option value, CH The option market price, Cm, lies between CL and cH. The bisection estimate is given as the linear interpolation between the two estimates: v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L)) Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy. Implied Volatility: Newton-Raphson Method The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility. Let v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv(i)) until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility, E is the desired degree of accuracy, c(m) is the market price of the option, and dc/dv(i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility). Numerical Greeks or Greeks by Finite Difference Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs) Things to know Only works on the daily timeframe and for the current source price. You can adjust the text size to fit the screen
Pine Script®指标
由loxx提供
Boyle Trinomial Options Pricing Model [Loxx]Boyle Trinomial Options Pricing Model is an options pricing indicator that builds an N-order trinomial tree to price American and European options. This is different form the Binomial model in that the Binomial assumes prices can only go up and down wheres the Trinomial model assumes prices can go up, down, or sideways (shoutout to the "crab" market enjoyers). This method also allows for dividend adjustment. The Trinomial Tree via VinegarHill Finance Labs A two-jump process for the asset price over each discrete time step was developed in the binomial lattice. Boyle expanded this frame of reference and explored the feasibility of option valuation by allowing for an extra jump in the stochastic process. In keeping with Black Scholes, Boyle examined an asset (S) with a lognormal distribution of returns. Over a small time interval, this distribution can be approximated by a three-point jump process in such a way that the expected return on the asset is the riskless rate, and the variance of the discrete distribution is equal to the variance of the corresponding lognormal distribution. The three point jump process was introduced by Phelim Boyle (1986) as a trinomial tree to price options and the effect has been momentous in the finance literature. Perhaps shamrock mythology or the well-known ballad associated with Brendan Behan inspired the Boyle insight to include a third jump in lattice valuation. His trinomial paper has spawned a huge amount of ground breaking research. In the trinomial model, the asset price S is assumed to jump uS or mS or dS after one time period (dt = T/n), where u > m > d. Joshi (2008) point out that the trinomial model is characterized by the following five parameters: (1) the probability of an up move pu, (2) the probability of an down move pd, (3) the multiplier on the stock price for an up move u, (4) the multiplier on the stock price for a middle move m, (5) the multiplier on the stock price for a down move d. A recombining tree is computationally more efficient so we require: ud = m*m M = exp (r∆t), V = exp (σ 2∆t), dt or ∆t = T/N where where N is the total number of steps of a trinomial tree. For a tree to be risk-neutral, the mean and variance across each time steps must be asymptotically correct. Boyle (1986) chose the parameters to be: m = 1, u = exp(λσ√ ∆t), d = 1/u pu =( md − M(m + d) + (M^2)*V )/ (u − d)(u − m) , pd =( um − M(u + m) + (M^2)*V )/ (u − d)(m − d) Boyle suggested that the choice of value for λ should exceed 1 and the best results were obtained when λ is approximately 1.20. One approach to constructing trinomial trees is to develop two steps of a binomial in combination as a single step of a trinomial tree. This can be engineered with many binomials CRR(1979), JR(1979) and Tian (1993) where the volatility is constant. Further reading: A Lattice Framework for Option Pricing with Two State Trinomial tree via wikipedia Inputs Spot price: select from 33 different types of price inputs Calculation Steps: how many iterations to be used in the Trinomial model. In practice, this number would be anywhere from 5000 to 15000, for our purposes here, this is limited to 220. Strike Price: the strike price of the option you're wishing to model Market Price: this is the market price of the option; choose, last, bid, or ask to see different results Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Trinomial model, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country % Manual Risk-free Rate: here you can manually enter the risk-free rate Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate % Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield Adjust for Dividends?: choose if you even want to use use dividends Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation Time Now Type: choose how you want to calculate time right now, see the tool tip Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours Expiry date settings: here you can specify the exact time the option expires Included Option pricing panel Loxx's Expanded Source Types Related indicators Implied Volatility Estimator using Black Scholes Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Pine Script®指标
由loxx提供
Implied Volatility Estimator using Black Scholes [Loxx]Implied Volatility Estimator using Black Scholes derives a estimation of implied volatility using the Black Scholes options pricing model. The Bisection algorithm is used for our purposes here. This includes the ability to adjust for dividends. Implied Volatility The implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of that option. The VIX , in contrast, is a model-free estimate of Implied Volatility. The latter is viewed as being important because it represents a measure of risk for the underlying asset. Elevated Implied Volatility suggests that risks to underlying are also elevated. Ordinarily, to estimate implied volatility we rely upon Black-Scholes (1973). This implies that we are prepared to accept the assumptions of Black Scholes (1973). Inputs Spot price: select from 33 different types of price inputs Strike Price: the strike price of the option you're wishing to model Market Price: this is the market price of the option; choose, last, bid, or ask to see different results Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Bisection algo, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country % Manual Risk-free Rate: here you can manually enter the risk-free rate Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate % Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield Adjust for Dividends?: choose if you even want to use use dividends Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation Time Now Type: choose how you want to calculate time right now, see the tool tip Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours Expiry date settings: here you can specify the exact time the option expires *** the algorithm inputs for low and high aren't to be changed unless you're working through the mathematics of how Bisection works. Included Option pricing panel Loxx's Expanded Source Types Related Indicators Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Pine Script®指标
由loxx提供
1
ATR and IV Volatility TableThis is a volatility tool designed to get the daily bottom and top values calculated using a daily ATR and IV values. ATR values can be calculated directly, however for IV I recommend to take the values from external sources for the asset that you want to trade. Regarding of the usage, I always recommend to go at the end of the previous close day of the candle(with replay function) or beginning of the daily open candle and get the expected values for movements. For example for 26April for SPX, we have an ATR of 77 points and the close of the candle was 4296. So based on ATR for 27 April our TOP is going to be 4296 + 77 , while our BOT is going to be 4296-77 At the same time lets assume the IV for today is going to be around 25% -> this is translated to 25 / (sqrt (252)) = 1.57 aprox So based on IV our TOP is going to be 4296 + 4296 * 0.0157 , while our BOT is going to be 4296 - 4296 * 0.0157 I found out from my calculations that 80-85% of the times these bot and top points act as an amazing support and resistence points for day trading, so I fully recommend you to start including them into your analysis. If you have any questions let me know !
Pine Script®指标
由exlux提供
4
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. ----- 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.
Pine Script®指标
由taylor_o提供
2
vol_premiaThis script shows the volatility risk premium for several instruments. The premium is simply "IV30 - RV20". Although Tradingview doesn't provide options prices, CBOE publishes 30-day implied volatilities for many instruments (most of which are VIX variations). CBOE calculates these in a standard way, weighting at- and out-of-the-money IVs for options that expire in 30 days, on average. For realized volatility, I used the standard deviation of log returns. Since there are twenty trading periods in 30 calendar days, IV30 can be compared to RV20. The "premium" is the difference, which reflects market participants' expectation for how much upcoming volatility will over- or under-shoot recent volatility. The script loads pretty slow since there are lots of symbols, so feel free to delete the ones you don't care about. Hopefully the code is straightforward enough. I won't list the meaning of every symbols here, since I might change them later, but you can type them into tradingview for data, and read about their volatility index on CBOE's website. Some of the more well-known ones are: ES: S&P futures, which I prefer to the SPX index). Its implied volatility is VIX. USO: the oil ETF representing WTI future prices. Its IV is OVX. GDX: the gold miner's ETF, which is usually more volatile than gold. Its IV is VXGDX. FXI: a china ETF, whose volatility is VXFXI. And so on. In addition to the premium, the "percentile" column shows where this premium ranks among the previous 252 trading days. 100 = the highest premium, 0 = the lowest premium.
Pine Script®指标
由taylor_o提供
vx_termsUSAGE -------- This script helps train your intuition for changes in the VX term structure. I recommend using it on the VIX chart, so you can compare changes in the terms to changes in VIX. It's also nice for calendar spread traders who want to get a feel for the same changes. 1. Select a day, month, and year using the inputs 2. Observe the data table. 3. Open the input again and increment or decrement the day (and month, year as necessary). 4. Click "Ok". 5. Click to deselect the indicator, which allows the chart to load new data. 6. The data table will be reloaded with the next/previous day's data. The data table has the following columns: - contract: the VX contracts, in sequence. refer to the CBOE for month codes (F for January, etc.) - close: the closing price of the contract. - ma:mb: the spread (difference) between this row and the next row. - ma:mb chg: the spread's change from prior close. For example, given the following values for the first two columns: VXQ2021, 16.5, -3.1, -0.2 VXU2021, 19.6, ..., ... The front month (Q = august) closed at 16.5, $3.1 below the s\September contract. The negative spread enlarged by $0.20 from $2.90 on the previous trading day. BUGS, ODDITIES, AND LIMITATIONS: ------------------------------------------- - The first column will be greyed out after expiration day, which is the 3rd Tuesday of that month. Unfortunately, I can't load the next month's contract due to some limitations with TV. - The active date is highlighted with a yellow background. When a non-trading date is selected, the highlight will disappear. However, the data table will sometimes fill with the nearest trading date, prematurely. No worries, just know that the data is probably for the previous Friday. - The script is clunky and slow, but this is the best I can do with TV. Hopefully they add more continuous contracts or allow true dynamic symbol loading. SPECIAL THANKS: --------------------- Thanks to HeWhoMustNotBeNamed for helping me get through some messiness. Very helpful guy. www.tradingview.com
Pine Script®指标
由taylor_o提供
1
vol_bracketThis simple script shows an "N" standard deviation volatility bracket, anchored at the opening price of the current month, week, or quarter. This anchor is meant to coincide roughly with the expiration of options issued at the same interval. You can choose between a manually-entered IV or the hv30 volatility model. Unlike my previous scripts, which all show the volatility bracket as a rolling figure, the anchor helps to visualize the volatility estimate in relation to price as it ranges over the (approximate) lifetime of a single, real contract.
Pine Script®指标
由taylor_o提供
3
VIX Implied Move Bands for ES/Emini futuresThis script uses the close of the VIX on a daily resolution to provide the 'implied move' for the E-mini SP500 futures. While it can be applied to any equity index, it's crucial to know that the VIX is calculated using SPX options, and may not reflect the implied volatility of other indices. The user can adjust the length of the moving average used to calculate the bands, the window of days used to calculate the implied move, and the multiplier that effects the width of the bands.
Pine Script®指标
由CSC1提供
7
Implied Volatility PercentileThis script calculates the Implied Volatility (IV) based on the daily returns of price using a standard deviation. It then annualizes the 30 day average to create the historical Implied Volatility. This indicator is intended to measure the IV for options traders but could also provide information for equities traders to show how price is extended in the expected price range based on the historical volatility. The IV Rank (Green line) is then calculated by looking at the high and low volatility over the number of days back specified in the input parameter, default is 252 (trading days in 1 year) and then calculating the rank of the current IV compared to the High and Low. This is not as reliable as the IV Percentile as the and extreme high or low could have a side effect on the ranking but it is included for those that want to use. The IV Percentile is calculated by counting the number of days below the current IV, then returns this as a % of the days back in the input You can adjust the number of days back to check the IV Rank & IV Percentile if you are not wanting to look back a whole year. This will only work on Daily or higher timeframe charts.
Pine Script®指标
由karimka提供
9
IV/HV Ratio's [Nic]IV is implied volatility HV is historic realized volatility Seneca teaches that we often suffer more in our minds than in reality, and the same is true with the stock market. This indicator can help identify when people are over paying for implied volatility relative to real volatility . This means that short sellers are over paying for puts and can be squeezed into covering their positions, resulting in a massive rally. The indicator can track this spread over many time frames, when the short time frame is much higher than the lower time frames, consider it a signal-of-interest.
Pine Script®指标
由NicTheMajestic提供
7
Implied Volatility SuiteThis is an updated, more robust, and open source version of my 2 previous scripts : "Implied Volatility Rank & Model-Free IVR" and "IV Rank & IV Percentile". This specific script provides you with 4 different types of volatility data: 1)Implied volatility, 2) Implied Volatility Rank, 3)Implied Volatility Percentile, 4)Skew Index. 1) Implied Volatility is the market's forecast of a likely movement, usually 1 standard deviation, in a securities price. 2) Implied Volatility Rank, ranks IV in relation to its high and low over a certain period of time. For example if over the past year IV had a high of 20% and a low of 10% and is currently 15%; the IV rank would be 50%, as 15 is 50% of the way between 10 & 20. IV Rank is mean reverting, meaning when IV Rank is high (green) it is assumed that future volatility will decrease; while if IV rank is low (red) it is assumed that future volatility will increase. 3) Implied Volatility Percentile ranks IV in relation to how many previous IV data points are less than the current value. For example if over the last 5 periods Implied volatility was 10%,12%,13%,14%,20%; and the current implied volatility is 15%, the IV percentile would be 80% as 4 out of the 5 previous IV values are below the current IV of 15%. IV Percentile is mean reverting, meaning when IV Percentile is high (green) it is assumed that future volatility will decrease; while if IV percentile is low (red) it is assumed that future volatility will increase. IV Percentile is more robust than IV Rank because, unlike IV Rank which only looks at the previous highs and lows, IV Percentile looks at all data points over the specified time period. 4)The skew index is an index I made that looks at volatility skew. Volatility Skew compares implied volatility of options with downside strikes versus upside strikes. If downside strikes have higher IV than upside strikes there is negative volatility skew. If upside strikes have higher IV than downside strikes then there is positive volatility skew. Typically, markets have a negative volatility skew, this has been the case since Black Monday in 1987. All negative skew means is that projected option contract prices tend to go down over time regardless of market conditions. Additionally, this script provides two ways to calculate the 4 data types above: a)Model-Based and b)VixFix. a) The Model-Based version calculates the four data types based on a model that projects future volatility. The reason that you would use this version is because it is what is most commonly used to calculate IV, IV Rank, IV Percentile, and Skew; and is closest to real world IV values. This version is what is referred to when people normally refer to IV. Additionally, the model version of IV, Rank, Percentile, and Skew are directionless. b) The VixFix version calculates the four data types based on the VixFix calculation. The reason that you would use this version is because it is based on past price data as opposed to a model, and as such is more sensitive to price action. Additionally, because the VixFix is meant to replicate the VIX Index (except it can be applied to any asset) it, just like the real VIX, does have a directional element to it. Because of this, VixFix IV, Rank, and Percentile tend to increase as markets move down, and decrease as markets move up. VixFix skew, on the other hand, is directionless. How to use this suite of tools: 1st. Pick the way you want your data calculated: either Model-Based or VixFix. 2nd. Input the various length parameters according to their labels: If you're using the model-based version and are trading options input your time til expiry, including weekends and holidays. You can do so in terms of days, hours, and minutes. If you're using the model-based version but aren't trading options you can just use the default input of 365 days. If you're using the VixFix version, input how many periods of data you want included in the calculation, this is labeled as "VixFix length". The default value used in this script is 252. 3rd. Finally, pick which data you want displayed from the dropdown menu: Implied Volatility, IV Rank, IV Percentile, or Volatility Skew Index.
Pine Script®指标
由SegaRKO提供
44
Black-Scholes Options Pricing ModelThis is an updated version of my "Black-Scholes Model and Greeks for European Options" indicator, that i previously published. I decided to make this updated version open-source, so people can tweak and improve it. The Black-Scholes model is a mathematical model used for pricing options. From this model you can derive the theoretical fair value of an options contract. Additionally, you can derive various risk parameters called Greeks. This indicator includes three types of data: Theoretical Option Price (blue), the Greeks (green), and implied volatility (red); their values are presented in that order. 1) Theoretical Option Price: This first value gives only the theoretical fair value of an option with a given strike based on the Black-Scholes framework. Remember this is a model and does not reflect actual option prices, just the theoretical price based on the Black-Scholes model and its parameters and assumptions. 2)Greeks (all of the Greeks included in this indicator are listed below): a)Delta is the rate of change of the theoretical option price with respect to the change in the underlying's price. This can also be used to approximate the probability of your option expiring in the money. For example, if you have an option with a delta of 0.62, then it has about a 62% chance of expiring in-the-money. This number runs from 0 to 1 for Calls, and 0 to -1 for Puts. b)Gamma is the rate of change of delta with respect to the change in the underlying's price. c)Theta, aka "time decay", is the rate of change in the theoretical option price with respect to the change in time. Theta tells you how much an option will lose its value day by day. d) Vega is the rate of change in the theoretical option price with respect to change in implied volatility . e)Rho is the rate of change in the theoretical option price with respect to change in the risk-free rate. Rho is rarely used because it is the parameter that options are least effected by, it is more useful for longer term options, like LEAPs. f)Vanna is the sensitivity of delta to changes in implied volatility . Vanna is useful for checking the effectiveness of delta-hedged and vega-hedged portfolios. g)Charm, aka "delta decay", is the instantaneous rate of change of delta over time. Charm is useful for monitoring delta-hedged positions. h)Vomma measures the sensitivity of vega to changes in implied volatility . i)Veta measures the rate of change in vega with respect to time. j)Vera measures the rate of change of rho with respect to implied volatility . k)Speed measures the rate of change in gamma with respect to changes in the underlying's price. Speed can be used when evaluating delta-hedged and gamma hedged portfolios. l)Zomma measures the rate of change in gamma with respect to changes in implied volatility . Zomma can be used to evaluate the effectiveness of a gamma-hedged portfolio. m)Color, aka "gamma decay", measures the rate of change of gamma over time. This can also be used to evaluate the effectiveness of a gamma-hedged portfolio. n)Ultima measures the rate of change in vomma with respect to implied volatility . o)Probability of Touch, is not a Greek, but a metric that I included, which tells you the probability of price touching your strike price before expiry. 3) Implied Volatility: This is the market's forecast of future volatility . Implied volatility is directionless, it cannot be used to forecast future direction. All it tells you is the forecast for future volatility. How to use this indicator: 1st. Input the strike price of your option. If you input a strike that is more than 3 standard deviations away from the current price, the model will return a value of n/a. 2nd. Input the current risk-free rate.(Including this is optional, because the risk-free rate is so small, you can just leave this number at zero.) 3rd. Input the time until expiry. You can enter this in terms of days, hours, and minutes. 4th.Input the chart time frame you are using in terms of minutes. For example if you're using the 1min time frame input 1, 4 hr time frame input 480, daily time frame input 1440, etc. 5th. Pick what style of option you want data for, European Vanilla or Binary. 6th. Pick what type of option you want data for, Long Call or Long Put. 7th . Finally, pick which Greek you want displayed from the drop-down list. *Remember the Option price presented, and the Greeks presented, are theoretical in nature, and not based upon actual option prices. Also, remember the Black-Scholes model is just a model based upon various parameters, it is not an actual representation of reality, only a theoretical one. *Note 1. If you choose binary, only data for Long Binary Calls will be presented. All of the Greeks for Long Binary Calls are available, except for rho and vera because they are negligible. *Note 2. Unlike vanilla european options, the delta of a binary option cannot be used to approximate the probability of the option expiring in-the-money. For binary options, if you want to approximate the probability of the binary option expiring in-the-money, use the price. The price of a binary option can be used to approximate its probability of expiring in-the-money. So if a binary option has a price of $40, then it has approximately a 40% chance of expiring in-the-money. *Note 3. As time goes on you will have to update the expiry, this model does not do that automatically. So for example, if you originally have an option with 30 days to expiry, tomorrow you would have to manually update that to 29 days, then the next day manually update the expiry to 28, and so on and so forth. There are various formulas that you can use to calculate the Greeks. I specifically chose the formulations included in this indicator because the Greeks that it presents are the closest to actual options data. I compared the Greeks given by this indicator to brokerage option data on a variety of asset classes from equity index future options to FX options and more. Because the indicator does not use actual option prices, its Greeks do not match the brokerage data exactly, but are close enough. I may try to make future updates that include data for Long Binary Puts, American Options, Asian Options, etc.
Pine Script®指标
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