Interpolation of term structure of implied volatility

Question

I have a dataset of options traded at each day, including the time to maturity, delta, strike price etc. Now I want to get the implied volatility of an option with time to maturity 30 days through interpolation of the term structure. My idea would be to

1. take the set of options on that day that have the closest time to maturity from above and below (e.g. 25 and 40 days)
2. fix the strike price
3. linearly interpolate the IV and the delta from these two points for a 30-day time to maturity

Could you tell me if this makes sense and if it is necessary to fix the strike?

Answer 1

There is a proper way to perform the IV term structure interpolation for a "continuous" 30-day implied volatility. Please refer to the steps below in the link:

How to compute 30/60/90-day Implied Volatility?

It is not too different from how CBOE computes their VIX measure.

But to answer your questions quickly, it makes the most sense to use an ATM option (delta = 0.5 and -0.5) for the linear interpolation across time. Therefore, you would actually have to do the interpolation across strikes first and then do the one across time. Again, please refer to the link for the proper steps.