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:

  1. Obtain OTM call and puts with deltas <0.5 and >-0.5, respectively.
  2. 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.
  3. Price 1001 options using the Black-Scholes formula.
  4. 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.
  5. 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.


1 Answer 1


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.

  • $\begingroup$ Wow, that's fast, that might be the answer to my question. Let me check with the OptionMetrics smoothed IV surface source :) $\endgroup$
    – KaiSqDist
    Mar 15 at 21:41
  • $\begingroup$ Thanks @phdstudent , one last question - Is the MFIV computed from 30-day options of monthly or annual frequency? $\endgroup$
    – KaiSqDist
    Mar 16 at 14:19
  • $\begingroup$ Sorry unsure if I understand the question. $\endgroup$
    – phdstudent
    Mar 16 at 16:41
  • $\begingroup$ When you compute the MFIV from the square root of the variance contract (which is computed using the volatility skew of 30-day options), is it of monthly or annual frequency? For example, when one computes the standard deviation of a 21 day historical rolling window of returns, one gets daily volatility and we multiply it by 252^0.5 to get annual volatility. If we multiply it by 21^0.5, we get monthly volatility instead. $\endgroup$
    – KaiSqDist
    Mar 16 at 17:09

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