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### Implied Volatility Calculator(Including hedging optimizer)

 Overview

 Implied volatility from option chains

The Implied Volatility Calculator calculates the implied volatility for each option in an option chain (option series).

Calculating implied volatility (IV) simultaneously for all options in a given series (or chain) is far more valuable than simply calculating the IVs for individual options (eg for an option you are considering trading).  This is because the real nature of implied volatility -- including any volatility skew, term structure, or market mispricing -- only becomes apparent when you compare the IVs of multiple options with a range of strikes and expiry dates side by side.

The Implied Volatility Calculator greatly simplifies this process. For each expiry month calls and puts are grouped together by strike so variations in implied volatility by call/put, strike (the volatility smile or volatility skew), by expiry month (term structure), or current market pricing anomalies can be easily observed.

An alternative analysis shows calls and puts for each strike side by side with in-the-money options highlighted, as in the example below.

 Volatility smile/skew analysis

The Implied Volatility Calculator produces a volatility surface for the entire option chain: a matrix showing the implied volatility by strike by expiry month.

Cubic spline interpolation is used to estimate the implied volatility for points on the surface for which no reliable market data are available.  (eg if no last price, or sensible  bid or ask prices are available). The implied volatility surface is presented in table form and graphically.  The graph can be dynamically rotated and tilted to enable the best view to be obtained of the way volatility varies by strike and expiry month.

For greater detail, a volatility smile chart lets you examine a cross section of the volatility skew surface.  One mouse click lets you move forward to the next month or backward to the previous month.  Calls and puts can be combined, as shown in the example below, or can be shown separately on the chart to highlight the differences between call and put IV, to visually identify skew crossover points etc. -- valuable information for spotting and evaluating volatility skew trading strategies.

 Volatility cones: comparing historical and implied volatilities

Volatility cones are produced by the IV calculator combining historical volatility with implied volatility on the one chart.

The IV calculator utilizes the Historical Volatility calculator interface to produce the statistical volatility cones, based on historical data from Yahoo finance, Quandl, or from a CSV file.

Strikes from the option chain are allocated to strike-range groups and implied volatility averaged within each group to iron out temporary market anomalies. Missing market data for individual strikes are filled in by cubic spline interpolation.

In the picture above the solid lines indicate statistical (historic) volatility -- maximum, minimum, current and upper and lower confidence levels for each time period -- and the "points" indicate the implied volatilities for time periods based on traded options.  Descriptions may be optionally "switched on" (or off)  separately for each strike range (as shown for one set of strikes in the above example) to simplify interpretation.

Comparing statistical forecasts of volatility with implied volatilities over time horizons equal to the terms of the options can help evaluate whether options are currently cheap or expensive. The volatility cone format shows clearly how the history of realized volatility compares with the market's forecast of volatility -- implied volatility --  over the same time periods.

 Valuation analysis

An analysis of the entire option chain, comparing market prices with theoretical option prices using user-defined assumptions for volatility, interest rate, and dividend yield/payments is produced by the Implied Volatility Calculator.

The percentage difference between market prices and theoretical prices is shown on the analysis to provide an indication as to whether the options are currently cheap or expensive.  Volatility can be easily varied to assess the impact of changed assumptions on valuations and on the relative attractiveness of the options in the chain.

This analysis, like the others provides extremely useful information in its own right.  But being Excel-based with no password protection it also serves as a template, or example, for users who would like to develop their own analyses using the Derivative Add-in's pricing, volatility and data retrieval components.

The Implied Volatility Calculator can be used together with the  historic volatility calculator to gain a much deeper understanding of the most critical factor affecting profitable options trading.

 Hedging optimization

A hedging optimization component is included with the implied volatility calculator. The optimizer will:

 calculate hedge parameters ("Greeks") for each option in the option chain for which a valid implied volatility could be calculated (ie where there was either a sensible bid/ask or last price available) scan the entire options chain to identify the optimal combination of trades in the underlying and/or options required to meet specific hedge ratio targets. The hedge ratio targets can be specified in terms of delta, delta-gamma, vega, delta-vega, or delta-gamma-vega.

Four scenarios are returned by the function, each of which, in addition to meeting the specified hedge ratio targets with the minimum possible number of trades, will also meet supplementary targets. For example, maximizing the position theta of a delta and vega neutral portfolio (so the hedger can derive maximum benefit from time decay); or minimizing the outlay required to make a portfolio delta and gamma neutral.

To fine tune the optimization process additional constraints can be specified. For instance stipulating that no one option trade can exceed a specified dollar value, or excluding options from the optimization process if their deltas are less than, say, 0.1.

Given that there are normally tens of thousands, and sometimes hundreds of thousands, of combinations of option trades on any underlying which could meet specific hedging targets, the hedging optimizer provides a simple to use, but very effective, way of arriving at a sensible selection of options which meets the specific financial requirements and risk tolerances of the trader.

 Software Environment

System requirements for the Finance Add-in for Excel.

The Hoadley Finance Add-in for Excel must be installed before using the Implied Volatility Calculator.

The Excel application is not password protected.

 Sources of Data

Free equity option chains: Currently delayed on-line option chain information is available free of charge for the US Exchanges, the ASX, Euronext, Eurex and NSE (India).  Real-time option chains are available free of charge for options traded on the Montreal Exchange.

Note that no guarantee can be given that the on-line information providers will continue to provide information free of charge or that they will not change the format of their data in the future without notice.

Broker and subscription option chains: Real-time data is available from a number of sources including TD Ameritrade (US equity option chains), Interactive Brokers (US and many International markets (equity, index and futures option chains)),   Charles Schwab (US equity, and futures option chains), Tradier Brokerage (US equity option chains), and Weblink's BullSignal  (Australian equity option chains).

Crypto option chains: Real-time Crypto option chains on cryptocurrency futures traded on the Deribit Crypto Options and Futures Exchange, and crypto spot option chains on the Binance, OKX, Bit.com and Delta exchanges are also available free of charge

Importing data from other sources:  Option chains can also be imported from a simple comma delimited text file if you have access to data from providers not explicitly handled by the software.  The format of the text file is defined in the add-in's documentation, and a sample Excel application which illustrates how to create the text file from on-line option chain data is also available for download.

The Implied Volatility Calculator is included free of charge with the full version of the  Finance Add-in. It is not available with the trial version.