Computing Daily 30-Day Model-Free Implied Volatility
Summary
The document asks how to calculate a daily 30-day model-free implied volatility (MFIV) when listed options rarely have exactly 30 days to maturity. The described procedure selects out-of-the-money calls and puts by delta, fits a cubic spline to implied volatility across a moneyness grid, reprices options with Black-Scholes, and applies a variance-contract formula before taking the square root.
The response clarifies that the cited research used a smoothed volatility-surface file, rather than raw option quotes. Such a surface provides standardized maturities and delta points, with interpolation across strikes and maturities to supply the 30-day inputs. This explains how a fixed-maturity measure can be calculated each day even when no listed contract expires in exactly 30 days. The note points to a specific data construction approach but does not detail surface estimation, interpolation quality, market-data requirements, or alternative methods.
Key ideas
- A daily fixed-maturity MFIV can use standardized inputs from a smoothed implied-volatility surface.
- The cited procedure selects out-of-the-money calls and puts using delta thresholds.
- A volatility curve across moneyness is converted into option prices and then a variance-contract value.
- The square root of the variance-contract value gives the MFIV measure.
- The explanation does not assess the accuracy or robustness of the surface interpolation.
Tags
Full text
# How should I go about computing the 30-day model free implied volatility (MFIV) daily? # How should I go about computing the 30-day model free implied volatility (MFIV) daily? As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied Volatility and Skewness. A brief recap of the MFIV procedure is as follows: - Obtain OTM call and puts with deltas <0.5 and >-0.5, respectively. - Using their implied volatilities, perform a cubic spline for the volatility skew using the moneyness range of 1/3 to 3 with 1001 points in between. - Price 1001 options using the Black-Scholes formula. - Price the variance contract using the formula from Bakshi et al. (2003) Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options. - Take the root of the variance contract that is the MFIV. My question is - If we should use a 30-day set of OTM call and put options to compute a single 30-day MFIV measure, how can we go about computing this daily if there aren't 30-day TTM options everyday? From what I understand, one can interpolate for a 30-day IV daily using "surrounding" contracts How to compute 30/60/90-day Implied Volatility? but these only produce a single 30-day IV. How can I go about generating these multiple 30-day OTM call and put options on the days that they don't exist? Since options usually exist for a fixed maturity - like the 3rd Friday of every month. ## Answer by phdstudent (score 2, accepted) https://quant.stackexchange.com/a/78672 If you read carefully their paper they are not using the raw options data from OptionMetrics but the smoothed surface file: > We use the volatility surface file, which contains a smoothed implied- volatility surface for a range of standard maturities and a set of option delta points. From the surface file we select the out-of-the-money implied volatilities for calls and puts (we take implied volatilities for calls with deltas smaller than or equal to 0.5, and implied volatilities for puts with deltas bigger than -0.5) for a maturity of 30 days. This surface file interpolation to have a standard grid on strikes and maturity.
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