Estimating Option Implied Volatility by Moneyness
Summary
The document discusses ways to estimate a reference implied volatility (IV) for options at different moneyness levels, with the aim of identifying contracts whose market IV appears mispriced. For forward-looking average volatility, it points to variance swap and volatility swap strikes. For averages by strike and maturity, it suggests break-even volatilities, which produce a theoretical skew or surface from historical prices rather than a purely forward-looking estimate.
Other suggestions include comparing options in delta space to account for changes in spot and time, and considering vega weights when combining expiries. A separate approach is to filter for liquid contracts using bid-ask spreads or open interest, then fit a cubic spline to the IV skew and compare a contract's market IV with the fitted value. These are proposed approaches, not validated results; the document does not specify a complete weighting method or test whether any method reliably detects mispricing. Liquidity filters and historical estimates also have limits when applied to current market prices.
Key ideas
- Variance swap or volatility swap strikes can serve as forward-looking average volatility measures.
- Break-even volatilities can estimate average volatility by strike and maturity from historical prices.
- Expressing options in delta space may help account for spot moves and time passing.
- Vega weighting is suggested as a possible way to combine different expiries, but no formula is given.
- Filtering illiquid options and fitting a spline can provide a reference IV skew for comparison with market quotes.
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# Practical approach to get average option IV # Practical approach to get average option IV Is there a practical method to calculate some sort of average IV for each level of moneyness of equity options? I'm thinking of an algorithm to find mispriced options and do to so, we need to figure out what is the expected IV depending on the moneyness of the option. ## Answer by Frido (score 1) https://quant.stackexchange.com/a/81596 To find a forward looking average of IVs the most obvious approach is to calculate the variance swap strike or volatility swap strike. However, to calculate the average IV for each strike and time to maturity, which I think is your question, a practical approach is to compute so-called break-even volatilities. This is explained in Dupire & Verma's presentation titled "Break even volatilities". Note though that this is based on historical prices, i.e. this is a 'theoretical skew/surface' based on historical prices. ## Answer by Aditya Gupta (score 0) https://quant.stackexchange.com/a/76159 I am going to give you a basic idea as how to go about it, as I have not thought much on this. But you could the delta space, convert all options into their deltas, this will take care of both spot changes and time passing.If you are looking to model various expiries, some weighted measure should be introduced (I have no idea how, but check out weighted vega) ## Answer by KaiSqDist (score 0) https://quant.stackexchange.com/a/77741 I did some work with IV before, but am not an IV expert. Usually mispriced options are the ones that are less liquid i.e. ITM options (but usually not ATM or OTM). You could probably try to filter for liquid options using their bid-ask spreads, open interest etc. and use a cubic spline to extrapolate an IV skew. Then, you would have an "expected" IV based on the skew vs the actual IV from the markets.
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