# 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:

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.