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I'm trying to estimate the volatility surface of an especially illiquid options market; only ATM quotes are available (so Vanna-Volga approximation is not viable) for options on quarterly futures for the next year -- but I am working with ITM and OTM daily options that go on for the next seven years. So my questions are:

  1. How can I rescale my quarterly IV to a daily level -- especially given the seasonality of the power market?
  2. How can I create a volatility surface using just the ATM volatility and (presumably) the Greeks?

Your help is greatly appreciated!

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This is a hard problem with only very approximate solutions

That ATM vol is the typical daily move in case the underlying ends flat in 3 months - it has very little to do with the expected daily move tomorrow and especially the full 1-day implied distribution that you seem to need. You simply can't 'rescale' vol in the way you want - the 1 day and quarterly vol are very different things.

I would suggest you use realized variance/skew/kurtosis to try to gain extra information to build a 1-day distribution, doing something like fitting a skewed Student's-t to the realized data. (You would input your seasonality here). Then add a vol termstructure that matches the ATM IV data you have. I'm basically suggesting you add a VRP to the realized data.

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