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:
Buscar en scripts para "implied volatility"
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
Implied Volatility and Historical VolatilityThis indicator provides a visualization of two different volatility measures, aiding in understanding market perceptions and actual price movements. Remember to combine it with other technical analysis tools and risk management strategies for informed trading decisions. The two measures of volatility:
Implied Volatility: Based on the standard deviation of recent price changes, it represents the market's expectation of future volatility.
Historical Volatility: Measured by the daily high-low range as a percentage of the closing price, it reflects the actual volatility experienced recently. It is intended to be used along side the Mean and Standard Deviation Lines indicator.
Inputs:
Period (Days): Defines the number of past bars used to calculate both types of volatility.
Calculations:
Interpretation:
Comparing the lines: Divergence between the lines can indicate potential mispricing:
If the Implied Volatility is higher than the Historical Volatility, the market might be overestimating future volatility.
Conversely, if the Implied Volatility is lower, the market might be underestimating future volatility.
Monitoring trends: Track changes in both lines over time to identify potential shifts in volatility expectations or actual market behavior.
Limitations:
Assumes normality in price distribution, which may not always hold true.
Historical Volatility only reflects past behavior, not future expectations.
Consider other factors like market sentiment and news events for comprehensive volatility analysis.
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.
Implied Volatility LevelsOverview:
The Implied Volatility Levels Indicator is a powerful tool designed to visualize different levels of implied volatility on your trading chart. This indicator calculates various implied volatility levels based on historical price data and plots them as dynamic dotted lines, helping traders identify significant market thresholds and potential reversal points.
Features:
Multi-Level Implied Volatility: The indicator calculates and plots multiple levels of implied volatility, including the mean and both positive and negative standard deviation multiples.
Dynamic Updates: The levels update in real-time, reflecting the latest market conditions without cluttering your chart with outdated information.
Customizable Parameters: Users can adjust the lookback period and the standard deviation multiplier to tailor the indicator to their trading strategy.
Visual Clarity: Implied volatility levels are displayed using distinct colors and dotted lines, providing clear visual cues without obstructing the view of price action.
Support for Multiple Levels: Includes additional levels (up to ±5 standard deviations) for in-depth market analysis.
How It Works:
The indicator computes the standard deviation of the closing prices over a user-defined lookback period. It then calculates various implied volatility levels by adding and subtracting multiples of this standard deviation from the mean price. These levels are plotted as dotted lines on the chart, offering traders a clear view of the current market's volatility landscape.
Usage:
Identify Key Levels: Use the plotted lines to spot potential support and resistance levels based on implied volatility.
Analyze Market Volatility: Understand how volatile the market is relative to historical data.
Plan Entry and Exit Points: Make informed trading decisions by observing where the price is in relation to the implied volatility levels.
Parameters:
Lookback Period (Days): The number of days to consider for calculating historical volatility (default is 252 days).
Standard Deviation Multiplier: A multiplier to adjust the distance of the levels from the mean (default is 1.0).
This indicator is ideal for traders looking to incorporate volatility analysis into their technical strategy, providing a robust framework for anticipating market movements and potential reversals.
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.
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.
Expected Move by Option's Implied Volatility High Liquidity
This script plots boxes to reflect weekly, monthly and yearly expected moves based on "At The Money" put and call option's implied volatility.
Symbols in range: This script will display Expected Move data for Symbols with high option liquidity.
Weekly Updates: Each weekend, the script is updated with fresh expected move data, a job that takes place every Saturday following the close of the markets on Friday.
In the provided script, several boxes are created and plotted on a price chart to represent the expected price moves for various timeframes.
These boxes serve as visual indicators to help traders and analysts understand the expected price volatility.
Definition of Expected Move: Expected Move refers to the anticipated range within which the price of an underlying asset is expected to move over a specific time frame, based on the current implied volatility of its options. Calculation: Expected Move is typically calculated by taking the current stock price and applying a multiple of the implied volatility. The most commonly used multiple is the one-standard-deviation move, which encompasses approximately 68% of potential price outcomes.
Example: Suppose a stock is trading at $100, and the implied volatility of its options is 20%. The one-standard-deviation expected move would be $100 * 0.20 = $20.
This suggests that there is a 68% probability that the stock's price will stay within a range of $80 to $120 over the specified time frame. Usage: Traders and investors use the expected move as a guideline for setting trading strategies and managing risk. It helps them gauge the potential price swings and make informed decisions about buying or selling options.There is a 68% chance that the underlying asset stock or ETF price will be within the boxed area at option expiry. The data on this script is updating weekly at the close of Friday, calculating the implied volatility for the week/month/year based on the "at the money" put and call options with the relevant expiry. This script will display Expected Move data for Symbols within the range of JBL-NOTE in alphabetical order.
In summary, implied volatility reflects market expectations about future price volatility, especially in the context of options. Expected Move is a practical application of implied volatility, helping traders estimate the likely price range for an asset over a given period. Both concepts play a vital role in assessing risk and devising trading strategies in the options and stock markets.
Expected Move by Option's Implied Volatility Symbols: EAT - GBDC
This script plots boxes to reflect weekly, monthly and yearly expected moves based on "At The Money" put and call option's implied volatility.
Symbols in range: This script will display Expected Move data for Symbols within the range of EAT-GDBC in alphabetical order.
Weekly Updates: Each weekend, the script is updated with fresh expected move data, a job that takes place every Saturday following the close of the markets on Friday.
In the provided script, several boxes are created and plotted on a price chart to represent the expected price moves for various timeframes.
These boxes serve as visual indicators to help traders and analysts understand the expected price volatility.
Definition of Expected Move: Expected Move refers to the anticipated range within which the price of an underlying asset is expected to move over a specific time frame, based on the current implied volatility of its options. Calculation: Expected Move is typically calculated by taking the current stock price and applying a multiple of the implied volatility. The most commonly used multiple is the one-standard-deviation move, which encompasses approximately 68% of potential price outcomes.
Example: Suppose a stock is trading at $100, and the implied volatility of its options is 20%. The one-standard-deviation expected move would be $100 * 0.20 = $20.
This suggests that there is a 68% probability that the stock's price will stay within a range of $80 to $120 over the specified time frame. Usage: Traders and investors use the expected move as a guideline for setting trading strategies and managing risk. It helps them gauge the potential price swings and make informed decisions about buying or selling options. There is a 68% chance that the underlying asset stock or ETF price will be within the boxed area at option expiry. The data on this script is updating weekly at the close of Friday, calculating the implied volatility for the week/month/year based on the "at the money" put and call options with the relevant expiry.
In summary, implied volatility reflects market expectations about future price volatility, especially in the context of options. Expected Move is a practical application of implied volatility, helping traders estimate the likely price range for an asset over a given period. Both concepts play a vital role in assessing risk and devising trading strategies in the options and stock markets.
Expected Move by Option's Implied Volatility Symbols: CLFD-EARN This script plots boxes to reflect weekly, monthly and yearly expected moves based on "At The Money" put and call option's implied volatility.
Symbols in range: This script will display Expected Move data for Symbols within the range of CLFD - EARN in alphabetical order.
Weekly Updates: Each weekend, the script is updated with fresh expected move data, a job that takes place every Saturday following the close of the markets on Friday.
In the provided script, several boxes are created and plotted on a price chart to represent the expected price moves for various timeframes.
These boxes serve as visual indicators to help traders and analysts understand the expected price volatility.
Definition of Expected Move: Expected Move refers to the anticipated range within which the price of an underlying asset is expected to move over a specific time frame, based on the current implied volatility of its options. Calculation: Expected Move is typically calculated by taking the current stock price and applying a multiple of the implied volatility. The most commonly used multiple is the one-standard-deviation move, which encompasses approximately 68% of potential price outcomes.
Example: Suppose a stock is trading at $100, and the implied volatility of its options is 20%. The one-standard-deviation expected move would be $100 * 0.20 = $20.
This suggests that there is a 68% probability that the stock's price will stay within a range of $80 to $120 over the specified time frame. Usage: Traders and investors use the expected move as a guideline for setting trading strategies and managing risk. It helps them gauge the potential price swings and make informed decisions about buying or selling options. There is a 68% chance that the underlying asset stock or ETF price will be within the boxed area at option expiry. The data on this script is updating weekly at the close of Friday, calculating the implied volatility for the week/month/year based on the "at the money" put and call options with the relevant expiry.
In summary, implied volatility reflects market expectations about future price volatility, especially in the context of options. Expected Move is a practical application of implied volatility, helping traders estimate the likely price range for an asset over a given period. Both concepts play a vital role in assessing risk and devising trading strategies in the options and stock markets.
Expected Move by Option's Implied Volatility Symbols: B - CLF
This script plots boxes to reflect weekly, monthly and yearly expected moves based on "At The Money" put and call option's implied volatility.
Symbols in range: This script will display Expected Move data for Symbols within the range of B - CLF in alphabetical order.
Weekly Updates: Each weekend, the script is updated with fresh expected move data, a job that takes place every Saturday following the close of the markets on Friday.
In the provided script, several boxes are created and plotted on a price chart to represent the expected price moves for various timeframes.
These boxes serve as visual indicators to help traders and analysts understand the expected price volatility.
Definition of Expected Move: Expected Move refers to the anticipated range within which the price of an underlying asset is expected to move over a specific time frame, based on the current implied volatility of its options. Calculation: Expected Move is typically calculated by taking the current stock price and applying a multiple of the implied volatility. The most commonly used multiple is the one-standard-deviation move, which encompasses approximately 68% of potential price outcomes.
Example: Suppose a stock is trading at $100, and the implied volatility of its options is 20%. The one-standard-deviation expected move would be $100 * 0.20 = $20.
This suggests that there is a 68% probability that the stock's price will stay within a range of $80 to $120 over the specified time frame. Usage: Traders and investors use the expected move as a guideline for setting trading strategies and managing risk. It helps them gauge the potential price swings and make informed decisions about buying or selling options. There is a 68% chance that the underlying asset stock or ETF price will be within the boxed area at option expiry. The data on this script is updating weekly at the close of Friday, calculating the implied volatility for the week/month/year based on the "at the money" put and call options with the relevant expiry.
In summary, implied volatility reflects market expectations about future price volatility, especially in the context of options. Expected Move is a practical application of implied volatility, helping traders estimate the likely price range for an asset over a given period. Both concepts play a vital role in assessing risk and devising trading strategies in the options and stock markets.
Expected Move by Option's Implied Volatility Symbols: A - AZZ
This script plots boxes to reflect weekly, monthly and yearly expected moves based on "At The Money" put and call option's implied volatility.
Symbols in range: This script will display Expected Move data for Symbols within the range of A - AZZ in alphabetical order.
Weekly Updates: Each weekend, the script is updated with fresh expected move data, a job that takes place every Saturday following the close of the markets on Friday.
In the provided script, several boxes are created and plotted on a price chart to represent the expected price moves for various timeframes.
These boxes serve as visual indicators to help traders and analysts understand the expected price volatility.
Definition of Expected Move: Expected Move refers to the anticipated range within which the price of an underlying asset is expected to move over a specific time frame, based on the current implied volatility of its options. Calculation: Expected Move is typically calculated by taking the current stock price and applying a multiple of the implied volatility. The most commonly used multiple is the one-standard-deviation move, which encompasses approximately 68% of potential price outcomes.
Example: Suppose a stock is trading at $100, and the implied volatility of its options is 20%. The one-standard-deviation expected move would be $100 * 0.20 = $20.
This suggests that there is a 68% probability that the stock's price will stay within a range of $80 to $120 over the specified time frame. Usage: Traders and investors use the expected move as a guideline for setting trading strategies and managing risk. It helps them gauge the potential price swings and make informed decisions about buying or selling options. There is a 68% chance that the underlying asset stock or ETF price will be within the boxed area at option expiry. The data on this script is updating weekly at the close of Friday, calculating the implied volatility for the week/month/year based on the "at the money" put and call options with the relevant expiry.
In summary, implied volatility reflects market expectations about future price volatility, especially in the context of options. Expected Move is a practical application of implied volatility, helping traders estimate the likely price range for an asset over a given period. Both concepts play a vital role in assessing risk and devising trading strategies in the options and stock markets.
EWMA Implied Volatility based on Historical VolatilityVolatility is the most common measure of risk.
Volatility in this sense can either be historical volatility (one observed from past data), or it could implied volatility (observed from market prices of financial instruments.)
The main objective of EWMA is to estimate the next-day (or period) volatility of a time series and closely track the volatility as it changes.
The EWMA model allows one to calculate a value for a given time on the basis of the previous day's value.
The EWMA model has an advantage in comparison with SMA, because the EWMA has a memory.
The EWMA remembers a fraction of its past by a factor A, that makes the EWMA a good indicator of the history of the price movement if a wise choice of the term is made.
Full details regarding the formula :
www.investopedia.com
In this scenario, we are looking at the historical volatility using the anual length of 252 trading days and a monthly length of 21.
Once we apply all of that we are going to get the yearly volatility.
After that we just have to divide that by the square root of number of days in a year, or weeks in a year or months in a year in order to get the daily/weekly/monthly expected volatility.
Once we have the expected volatility, we can estimate with a high chance where the market top and bottom is going to be and continue our analysis on that premise.
If you have any questions, please let me know !
Wavetrend in Dynamic Zones with Kumo Implied VolatilityI was asked to do one of those, so here we go...
As always free and open source as it should be. Do not pay for such indicators!
A WaveTrend Indicator or also widely known as "Market Cipher" is an Indicator that is based on Moving Averages, therefore its an "lagging indicator". Lagging indicators are best used in combination with leading indicators. In this script the "leading indicator" component are Daily, Weekly or Monthly Pivots . These Pivots can be used as dynamic Support and Resistance , Stoploss, Take Profit etc.
This indicator combination is best used in larger timeframes. For lower timeframes you might need to change settings to your liking.
The general Wavetrend settings are the same that are used in Market Cipher, Market Liberator and such popular indicators.
What are these circles?
-These are the WaveTrend Divergences. Red for Regular-Bearish. Orange for Hidden-Bearish. Green for Regular-Bullish. Aqua for Hidden-Bullish.
What are these white, orange and aqua triangles?
-These are the WaveTrend Pivots. A Pivot counter was added. Every time a pivot is lower than the previous one, an orange triangle is printed, every time a pivot is higher than the previous one an aqua triangle is printed. That mimics a very common way Wavetrend is being used for trading when using those other paid Wavetrend indicators.
What are these Orange and Aqua Zones?
-These are Dynamic Zones based on the indicator itself, they offer more information than static zones. Of course static lines are also included and can be adjusted.
What are the lines between the waves?
-This is a Kumo Cloud Implied Volatility indicator. It is color coded and can be used to indicate if a major market move/bottom/top happened.
What are those numbers on the right?
-The first number is a Bollinger Band indicator that shows if said Bollinger Band is in a state of Oversold/Overbought, the second number is the actual Bollinger Band Width that indicates if the Bollinger Band squeezes, normally that happens right before the market makes an explosive move.
Please keep in mind that this indicator is a tool and not a strategy, do not blindly trade signals, do your own research first! Use this indicator in conjunction with other indicators to get multiple confirmations.
Kumo Implied VolatilityFrom ProRealCode www.prorealcode.com
"In my pursuit to quantify the Ichimoku indicator, I have tried to quantify implied volatility by measuring the Kumo thickness. Firstly, I took the absolute value of the distance between SpanA and SpanB, I then normalized the value and created standard deviation bands. Now I can compare the Kumo thickness with the average thickness over 200 periods. When the value goes above 100, it implies that the Kumo is thicker than 2 standard deviations of the average (there is therefore only a 5% chance that this happens). A reading over 100 might indicate trend exhaustion and a reading below 20 indicates low volatility and Kumo twists (I chose 20 only by observation and not statistical significance). Interestingly, this indicator sometime gives similar information to ADX. So far, the best use for this indicator is as a setup indicator for trend exhaustion or low volatility breakouts from Kumo twists. Extreme readings before Kumo breakouts looks interesting."
Bitcoin Implied VolatilityThis simple script collects data from FTX:BVOLUSD to plot BTC’s implied volatility as a standalone indicator instead of a chart.
Implied volatility is used to gauge future volatility and often used in options trading.
Implied Volatility Range ProjectionThis script plots an expected future range estimation based on implied volatilities, using a specified volatility index as proxy for ATM implied volatilities.
For example the S&P 500 could use the VIX.
My scriptImplied Volatility vs Historical Volatility
**Uncheck Plot box**
IV > HV = Overvalued
IV = HV = Fair Value
IV > HV = Undervalued
1. Pair with IV Rank: Use IV vs HV to confirm the setup, but IV Rank (50+, 70+) tells you how “high” IV is relative to its own history.
2. Timeframe: Use daily charts — IV is not meaningful on intraday timeframes.
3. Avoid noise: Use a smoothed HV (e.g., 20-day) and don’t chase small crossovers — look for clear divergence.
Volatility Risk Premium (VRP) 1.0ENGLISH
This indicator (V-R-P) calculates the (one month) Volatility Risk Premium for S&P500 and Nasdaq-100.
V-R-P is the premium hedgers pay for over Realized Volatility for S&P500 and Nasdaq-100 index options.
The premium stems from hedgers paying to insure their portfolios, and manifests itself in the differential between the price at which options are sold (Implied Volatility) and the volatility the S&P500 and Nasdaq-100 ultimately realize (Realized Volatility).
I am using 30-day Implied Volatility (IV) and 21-day Realized Volatility (HV) as the basis for my calculation, as one month of IV is based on 30 calendaristic days and one month of HV is based on 21 trading days.
At first, the indicator appears blank and a label instructs you to choose which index you want the V-R-P to plot on the chart. Use the indicator settings (the sprocket) to choose one of the indices (or both).
Together with the V-R-P line, the indicator will show its one year moving average within a range of +/- 15% (which you can change) for benchmarking purposes. We should consider this range the “normalized” V-R-P for the actual period.
The Zero Line is also marked on the indicator.
Interpretation
When V-R-P is within the “normalized” range, … well... volatility and uncertainty, as it’s seen by the option market, is “normal”. We have a “premium” of volatility which should be considered normal.
When V-R-P is above the “normalized” range, the volatility premium is high. This means that investors are willing to pay more for options because they see an increasing uncertainty in markets.
When V-R-P is below the “normalized” range but positive (above the Zero line), the premium investors are willing to pay for risk is low, meaning they see decreasing uncertainty and risks in the market, but not by much.
When V-R-P is negative (below the Zero line), we have COMPLACENCY. This means investors see upcoming risk as being lower than what happened in the market in the recent past (within the last 30 days).
CONCEPTS:
Volatility Risk Premium
The volatility risk premium (V-R-P) is the notion that implied volatility (IV) tends to be higher than realized volatility (HV) as market participants tend to overestimate the likelihood of a significant market crash.
This overestimation may account for an increase in demand for options as protection against an equity portfolio. Basically, this heightened perception of risk may lead to a higher willingness to pay for these options to hedge a portfolio.
In other words, investors are willing to pay a premium for options to have protection against significant market crashes even if statistically the probability of these crashes is lesser or even negligible.
Therefore, the tendency of implied volatility is to be higher than realized volatility, thus V-R-P being positive.
Realized/Historical Volatility
Historical Volatility (HV) is the statistical measure of the dispersion of returns for an index over a given period of time.
Historical volatility is a well-known concept in finance, but there is confusion in how exactly it is calculated. Different sources may use slightly different historical volatility formulas.
For calculating Historical Volatility I am using the most common approach: annualized standard deviation of logarithmic returns, based on daily closing prices.
Implied Volatility
Implied Volatility (IV) is the market's forecast of a likely movement in the price of the index and it is expressed annualized, using percentages and standard deviations over a specified time horizon (usually 30 days).
IV is used to price options contracts where high implied volatility results in options with higher premiums and vice versa. Also, options supply and demand and time value are major determining factors for calculating Implied Volatility.
Implied Volatility usually increases in bearish markets and decreases when the market is bullish.
For determining S&P500 and Nasdaq-100 implied volatility I used their volatility indices: VIX and VXN (30-day IV) provided by CBOE.
Warning
Please be aware that because CBOE doesn’t provide real-time data in Tradingview, my V-R-P calculation is also delayed, so you shouldn’t use it in the first 15 minutes after the opening.
This indicator is calibrated for a daily time frame.
ESPAŇOL
Este indicador (V-R-P) calcula la Prima de Riesgo de Volatilidad (de un mes) para S&P500 y Nasdaq-100.
V-R-P es la prima que pagan los hedgers sobre la Volatilidad Realizada para las opciones de los índices S&P500 y Nasdaq-100.
La prima proviene de los hedgers que pagan para asegurar sus carteras y se manifiesta en el diferencial entre el precio al que se venden las opciones (Volatilidad Implícita) y la volatilidad que finalmente se realiza en el S&P500 y el Nasdaq-100 (Volatilidad Realizada).
Estoy utilizando la Volatilidad Implícita (IV) de 30 días y la Volatilidad Realizada (HV) de 21 días como base para mi cálculo, ya que un mes de IV se basa en 30 días calendario y un mes de HV se basa en 21 días de negociación.
Al principio, el indicador aparece en blanco y una etiqueta le indica que elija qué índice desea que el V-R-P represente en el gráfico. Use la configuración del indicador (la rueda dentada) para elegir uno de los índices (o ambos).
Junto con la línea V-R-P, el indicador mostrará su promedio móvil de un año dentro de un rango de +/- 15% (que puede cambiar) con fines de evaluación comparativa. Deberíamos considerar este rango como el V-R-P "normalizado" para el período real.
La línea Cero también está marcada en el indicador.
Interpretación
Cuando el V-R-P está dentro del rango "normalizado",... bueno... la volatilidad y la incertidumbre, como las ve el mercado de opciones, es "normal". Tenemos una “prima” de volatilidad que debería considerarse normal.
Cuando V-R-P está por encima del rango "normalizado", la prima de volatilidad es alta. Esto significa que los inversores están dispuestos a pagar más por las opciones porque ven una creciente incertidumbre en los mercados.
Cuando el V-R-P está por debajo del rango "normalizado" pero es positivo (por encima de la línea Cero), la prima que los inversores están dispuestos a pagar por el riesgo es baja, lo que significa que ven una disminución, pero no pronunciada, de la incertidumbre y los riesgos en el mercado.
Cuando V-R-P es negativo (por debajo de la línea Cero), tenemos COMPLACENCIA. Esto significa que los inversores ven el riesgo próximo como menor que lo que sucedió en el mercado en el pasado reciente (en los últimos 30 días).
CONCEPTOS:
Prima de Riesgo de Volatilidad
La Prima de Riesgo de Volatilidad (V-R-P) es la noción de que la Volatilidad Implícita (IV) tiende a ser más alta que la Volatilidad Realizada (HV) ya que los participantes del mercado tienden a sobrestimar la probabilidad de una caída significativa del mercado.
Esta sobreestimación puede explicar un aumento en la demanda de opciones como protección contra una cartera de acciones. Básicamente, esta mayor percepción de riesgo puede conducir a una mayor disposición a pagar por estas opciones para cubrir una cartera.
En otras palabras, los inversores están dispuestos a pagar una prima por las opciones para tener protección contra caídas significativas del mercado, incluso si estadísticamente la probabilidad de estas caídas es menor o insignificante.
Por lo tanto, la tendencia de la Volatilidad Implícita es de ser mayor que la Volatilidad Realizada, por lo cual el V-R-P es positivo.
Volatilidad Realizada/Histórica
La Volatilidad Histórica (HV) es la medida estadística de la dispersión de los rendimientos de un índice durante un período de tiempo determinado.
La Volatilidad Histórica es un concepto bien conocido en finanzas, pero existe confusión sobre cómo se calcula exactamente. Varias fuentes pueden usar fórmulas de Volatilidad Histórica ligeramente diferentes.
Para calcular la Volatilidad Histórica, utilicé el enfoque más común: desviación estándar anualizada de rendimientos logarítmicos, basada en los precios de cierre diarios.
Volatilidad Implícita
La Volatilidad Implícita (IV) es la previsión del mercado de un posible movimiento en el precio del índice y se expresa anualizada, utilizando porcentajes y desviaciones estándar en un horizonte de tiempo específico (generalmente 30 días).
IV se utiliza para cotizar contratos de opciones donde la alta Volatilidad Implícita da como resultado opciones con primas más altas y viceversa. Además, la oferta y la demanda de opciones y el valor temporal son factores determinantes importantes para calcular la Volatilidad Implícita.
La Volatilidad Implícita generalmente aumenta en los mercados bajistas y disminuye cuando el mercado es alcista.
Para determinar la Volatilidad Implícita de S&P500 y Nasdaq-100 utilicé sus índices de volatilidad: VIX y VXN (30 días IV) proporcionados por CBOE.
Precaución
Tenga en cuenta que debido a que CBOE no proporciona datos en tiempo real en Tradingview, mi cálculo de V-R-P también se retrasa, y por este motivo no se recomienda usar en los primeros 15 minutos desde la apertura.
Este indicador está calibrado para un marco de tiempo diario.
Volatility Risk Premium GOLD & SILVER 1.0ENGLISH
This indicator (V-R-P) calculates the (one month) Volatility Risk Premium for GOLD and SILVER.
V-R-P is the premium hedgers pay for over Realized Volatility for GOLD and SILVER options.
The premium stems from hedgers paying to insure their portfolios, and manifests itself in the differential between the price at which options are sold (Implied Volatility) and the volatility GOLD and SILVER ultimately realize (Realized Volatility).
I am using 30-day Implied Volatility (IV) and 21-day Realized Volatility (HV) as the basis for my calculation, as one month of IV is based on 30 calendaristic days and one month of HV is based on 21 trading days.
At first, the indicator appears blank and a label instructs you to choose which index you want the V-R-P to plot on the chart. Use the indicator settings (the sprocket) to choose one of the precious metals (or both).
Together with the V-R-P line, the indicator will show its one year moving average within a range of +/- 15% (which you can change) for benchmarking purposes. We should consider this range the “normalized” V-R-P for the actual period.
The Zero Line is also marked on the indicator.
Interpretation
When V-R-P is within the “normalized” range, … well... volatility and uncertainty, as it’s seen by the option market, is “normal”. We have a “premium” of volatility which should be considered normal.
When V-R-P is above the “normalized” range, the volatility premium is high. This means that investors are willing to pay more for options because they see an increasing uncertainty in markets.
When V-R-P is below the “normalized” range but positive (above the Zero line), the premium investors are willing to pay for risk is low, meaning they see decreasing uncertainty and risks in the market, but not by much.
When V-R-P is negative (below the Zero line), we have COMPLACENCY. This means investors see upcoming risk as being lower than what happened in the market in the recent past (within the last 30 days).
CONCEPTS :
Volatility Risk Premium
The volatility risk premium (V-R-P) is the notion that implied volatility (IV) tends to be higher than realized volatility (HV) as market participants tend to overestimate the likelihood of a significant market crash.
This overestimation may account for an increase in demand for options as protection against an equity portfolio. Basically, this heightened perception of risk may lead to a higher willingness to pay for these options to hedge a portfolio.
In other words, investors are willing to pay a premium for options to have protection against significant market crashes even if statistically the probability of these crashes is lesser or even negligible.
Therefore, the tendency of implied volatility is to be higher than realized volatility, thus V-R-P being positive.
Realized/Historical Volatility
Historical Volatility (HV) is the statistical measure of the dispersion of returns for an index over a given period of time.
Historical volatility is a well-known concept in finance, but there is confusion in how exactly it is calculated. Different sources may use slightly different historical volatility formulas.
For calculating Historical Volatility I am using the most common approach: annualized standard deviation of logarithmic returns, based on daily closing prices.
Implied Volatility
Implied Volatility (IV) is the market's forecast of a likely movement in the price of the index and it is expressed annualized, using percentages and standard deviations over a specified time horizon (usually 30 days).
IV is used to price options contracts where high implied volatility results in options with higher premiums and vice versa. Also, options supply and demand and time value are major determining factors for calculating Implied Volatility.
Implied Volatility usually increases in bearish markets and decreases when the market is bullish.
For determining GOLD and SILVER implied volatility I used their volatility indices: GVZ and VXSLV (30-day IV) provided by CBOE.
Warning
Please be aware that because CBOE doesn’t provide real-time data in Tradingview, my V-R-P calculation is also delayed, so you shouldn’t use it in the first 15 minutes after the opening.
This indicator is calibrated for a daily time frame.
----------------------------------------------------------------------
ESPAŇOL
Este indicador (V-R-P) calcula la Prima de Riesgo de Volatilidad (de un mes) para GOLD y SILVER.
V-R-P es la prima que pagan los hedgers sobre la Volatilidad Realizada para las opciones de GOLD y SILVER.
La prima proviene de los hedgers que pagan para asegurar sus carteras y se manifiesta en el diferencial entre el precio al que se venden las opciones (Volatilidad Implícita) y la volatilidad que finalmente se realiza en el ORO y la PLATA (Volatilidad Realizada).
Estoy utilizando la Volatilidad Implícita (IV) de 30 días y la Volatilidad Realizada (HV) de 21 días como base para mi cálculo, ya que un mes de IV se basa en 30 días calendario y un mes de HV se basa en 21 días de negociación.
Al principio, el indicador aparece en blanco y una etiqueta le indica que elija qué índice desea que el V-R-P represente en el gráfico. Use la configuración del indicador (la rueda dentada) para elegir uno de los metales preciosos (o ambos).
Junto con la línea V-R-P, el indicador mostrará su promedio móvil de un año dentro de un rango de +/- 15% (que puede cambiar) con fines de evaluación comparativa. Deberíamos considerar este rango como el V-R-P "normalizado" para el período real.
La línea Cero también está marcada en el indicador.
Interpretación
Cuando el V-R-P está dentro del rango "normalizado",... bueno... la volatilidad y la incertidumbre, como las ve el mercado de opciones, es "normal". Tenemos una “prima” de volatilidad que debería considerarse normal.
Cuando V-R-P está por encima del rango "normalizado", la prima de volatilidad es alta. Esto significa que los inversores están dispuestos a pagar más por las opciones porque ven una creciente incertidumbre en los mercados.
Cuando el V-R-P está por debajo del rango "normalizado" pero es positivo (por encima de la línea Cero), la prima que los inversores están dispuestos a pagar por el riesgo es baja, lo que significa que ven una disminución, pero no pronunciada, de la incertidumbre y los riesgos en el mercado.
Cuando V-R-P es negativo (por debajo de la línea Cero), tenemos COMPLACENCIA. Esto significa que los inversores ven el riesgo próximo como menor que lo que sucedió en el mercado en el pasado reciente (en los últimos 30 días).
CONCEPTOS :
Prima de Riesgo de Volatilidad
La Prima de Riesgo de Volatilidad (V-R-P) es la noción de que la Volatilidad Implícita (IV) tiende a ser más alta que la Volatilidad Realizada (HV) ya que los participantes del mercado tienden a sobrestimar la probabilidad de una caída significativa del mercado.
Esta sobreestimación puede explicar un aumento en la demanda de opciones como protección contra una cartera de acciones. Básicamente, esta mayor percepción de riesgo puede conducir a una mayor disposición a pagar por estas opciones para cubrir una cartera.
En otras palabras, los inversores están dispuestos a pagar una prima por las opciones para tener protección contra caídas significativas del mercado, incluso si estadísticamente la probabilidad de estas caídas es menor o insignificante.
Por lo tanto, la tendencia de la Volatilidad Implícita es de ser mayor que la Volatilidad Realizada, por lo cual el V-R-P es positivo.
Volatilidad Realizada/Histórica
La Volatilidad Histórica (HV) es la medida estadística de la dispersión de los rendimientos de un índice durante un período de tiempo determinado.
La Volatilidad Histórica es un concepto bien conocido en finanzas, pero existe confusión sobre cómo se calcula exactamente. Varias fuentes pueden usar fórmulas de Volatilidad Histórica ligeramente diferentes.
Para calcular la Volatilidad Histórica, utilicé el enfoque más común: desviación estándar anualizada de rendimientos logarítmicos, basada en los precios de cierre diarios.
Volatilidad Implícita
La Volatilidad Implícita (IV) es la previsión del mercado de un posible movimiento en el precio del índice y se expresa anualizada, utilizando porcentajes y desviaciones estándar en un horizonte de tiempo específico (generalmente 30 días).
IV se utiliza para cotizar contratos de opciones donde la alta Volatilidad Implícita da como resultado opciones con primas más altas y viceversa. Además, la oferta y la demanda de opciones y el valor temporal son factores determinantes importantes para calcular la Volatilidad Implícita.
La Volatilidad Implícita generalmente aumenta en los mercados bajistas y disminuye cuando el mercado es alcista.
Para determinar la Volatilidad Implícita de GOLD y SILVER utilicé sus índices de volatilidad: GVZ y VXSLV (30 días IV) proporcionados por CBOE.
Precaución
Tenga en cuenta que debido a que CBOE no proporciona datos en tiempo real en Tradingview, mi cálculo de V-R-P también se retrasa, y por este motivo no se recomienda usar en los primeros 15 minutos desde la apertura.
Este indicador está calibrado para un marco de tiempo diario.
Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]Generalized Black-Scholes-Merton Option Pricing Formula is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks aka "Option Sensitivities" and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas".
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm, float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility (vega) when searching for the implied volatility. For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility, al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm, lies between CL and cH. The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility. Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv(i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility, E is the desired degree of accuracy, c(m) is the market price of the option, and dc/dv(i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility).
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Black Scholes Option Pricing Model w/ Greeks [Loxx]The Black Scholes Merton model
If you are new to options I strongly advise you to profit from Robert Shiller's lecture on same . It combines practical market insights with a strong authoritative grasp of key models in option theory. He explains many of the areas covered below and in the following pages with a lot intuition and relatable anecdotage. We start here with Black Scholes Merton which is probably the most popular option pricing framework, due largely to its simplicity and ease in terms of implementation. The closed-form solution is efficient in terms of speed and always compares favorably relative to any numerical technique. The Black–Scholes–Merton model is a mathematical go-to model for estimating the value of European calls and puts. In the early 1970’s, Myron Scholes, and Fisher Black made an important breakthrough in the pricing of complex financial instruments. Robert Merton simultaneously was working on the same problem and applied the term Black-Scholes model to describe new generation of pricing. The Black Scholes (1973) contribution developed insights originally proposed by Bachelier 70 years before. In 1997, Myron Scholes and Robert Merton received the Nobel Prize for Economics. Tragically, Fisher Black died in 1995. The Black–Scholes formula presents a theoretical estimate (or model estimate) of the price of European-style options independently of the risk of the underlying security. Future payoffs from options can be discounted using the risk-neutral rate. Earlier academic work on options (e.g., Malkiel and Quandt 1968, 1969) had contemplated using either empirical, econometric analyses or elaborate theoretical models that possessed parameters whose values could not be calibrated directly. In contrast, Black, Scholes, and Merton’s parameters were at their core simple and did not involve references to utility or to the shifting risk appetite of investors. Below, we present a standard type formula, where: c = Call option value, p = Put option value, S=Current stock (or other underlying) price, K or X=Strike price, r=Risk-free interest rate, q = dividend yield, T=Time to maturity and N denotes taking the normal cumulative probability. b = (r - q) = cost of carry. (via VinegarHill-Financelab )
Things to know
This can only be used on the daily timeframe
You must select the option type and the greeks you wish to show
This indicator is a work in process, functions may be updated in the future. I will also be adding additional greeks as I code them or they become available in finance literature. This indictor contains 18 greeks. Many more will be added later.
Inputs
Spot price: select from 33 different types of price inputs
Calculation Steps: how many iterations to be used in the BS model. In practice, this number would be anywhere from 5000 to 15000, for our purposes here, this is limited to 300
Strike Price: the strike price of the option you're wishing to model
% Implied Volatility: here you can manually enter implied volatility
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the BS process, this is to serve as a sort of benchmark for the implied volatility ,
Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these
Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country
% Manual Risk-free Rate: here you can manually enter the risk-free rate
Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate
% Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield
Adjust for Dividends?: choose if you even want to use use dividends
Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation
Time Now Type: choose how you want to calculate time right now, see the tool tip
Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc
Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours
Expiry date settings: here you can specify the exact time the option expires
The Black Scholes Greeks
The Option Greek formulae express the change in the option price with respect to a parameter change taking as fixed all the other inputs. ( Haug explores multiple parameter changes at once .) One significant use of Greek measures is to calibrate risk exposure. A market-making financial institution with a portfolio of options, for instance, would want a snap shot of its exposure to asset price, interest rates, dividend fluctuations. It would try to establish impacts of volatility and time decay. In the formulae below, the Greeks merely evaluate change to only one input at a time. In reality, we might expect a conflagration of changes in interest rates and stock prices etc. (via VigengarHill-Financelab )
First-order Greeks
Delta: Delta measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price. Delta is the first derivative of the value
Vega: Vegameasures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset.
Theta: Theta measures the sensitivity of the value of the derivative to the passage of time (see Option time value): the "time decay."
Rho: Rho measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term).
Lambda: Lambda, Omega, or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.
Epsilon: Epsilon, also known as psi, is the percentage change in option value per percentage change in the underlying dividend yield, a measure of the dividend risk. The dividend yield impact is in practice determined using a 10% increase in those yields. Obviously, this sensitivity can only be applied to derivative instruments of equity products.
Second-order Greeks
Gamma: Measures the rate of change in the delta with respect to changes in the underlying price. Gamma is the second derivative of the value function with respect to the underlying price.
Vanna: Vanna, also referred to as DvegaDspot and DdeltaDvol, is a second order derivative of the option value, once to the underlying spot price and once to volatility. It is mathematically equivalent to DdeltaDvol, the sensitivity of the option delta with respect to change in volatility; or alternatively, the partial of vega with respect to the underlying instrument's price. Vanna can be a useful sensitivity to monitor when maintaining a delta- or vega-hedged portfolio as vanna will help the trader to anticipate changes to the effectiveness of a delta-hedge as volatility changes or the effectiveness of a vega-hedge against change in the underlying spot price.
Charm: Charm or delta decay measures the instantaneous rate of change of delta over the passage of time.
Vomma: Vomma, volga, vega convexity, or DvegaDvol measures second order sensitivity to volatility. Vomma is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes.
Veta: Veta or DvegaDtime measures the rate of change in the vega with respect to the passage of time. Veta is the second derivative of the value function; once to volatility and once to time.
Vera: Vera (sometimes rhova) measures the rate of change in rho with respect to volatility. Vera is the second derivative of the value function; once to volatility and once to interest rate.
Third-order Greeks
Speed: Speed measures the rate of change in Gamma with respect to changes in the underlying price.
Zomma: Zomma measures the rate of change of gamma with respect to changes in volatility.
Color: Color, gamma decay or DgammaDtime measures the rate of change of gamma over the passage of time.
Ultima: Ultima measures the sensitivity of the option vomma with respect to change in volatility.
Dual Delta: Dual Delta determines how the option price changes in relation to the change in the option strike price; it is the first derivative of the option price relative to the option strike price
Dual Gamma: Dual Gamma determines by how much the coefficient will changedual delta when the option strike price changes; it is the second derivative of the option price relative to the option strike price.
Related Indicators
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Implied Volatility Estimator using Black Scholes
Boyle Trinomial Options Pricing Model
Black-Scholes 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.
