Building Daily Option Volatility Estimates from Quarterly ATM Quotes

Summary

The document considers how to estimate a volatility surface for illiquid daily options when the available market data consist only of at-the-money implied volatilities on quarterly futures. The options extend across a much longer horizon and include in-the-money and out-of-the-money strikes. The answer cautions that quarterly implied volatility cannot simply be rescaled to obtain a one-day volatility or distribution: the horizons describe different quantities, and quarterly ATM volatility says little about tomorrow’s move or its full implied distribution.

As an approximate alternative, the response proposes using realized variance, skew, and kurtosis to inform a one-day distribution, for example by fitting a skewed Student’s t distribution. Power-market seasonality can be incorporated into the realized-data estimates, then a volatility term structure can be added to match the available ATM implied-volatility quotes. This effectively combines realized behavior with a volatility risk premium. The answer stresses that the sparse data make the problem difficult and the resulting surface approximate; it does not specify a complete calibration procedure.

Key ideas

• Quarterly ATM implied volatility cannot be mechanically converted into a one-day implied distribution.
• Realized variance, skew, and kurtosis can provide additional information when option quotes are sparse.
• A skewed Student’s t distribution is suggested as one possible model for daily returns.
• Seasonality can be incorporated into estimates derived from realized market data.
• A volatility term structure can be added to align the estimate with available quarterly ATM quotes.

Tags

# Volatility surface of daily contracts from ATM volatility of quarterly contracts


# Volatility surface of daily contracts from ATM volatility of quarterly contracts












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:

- How can I rescale my quarterly IV to a daily level -- especially given the seasonality of the power market?

- How can I create a volatility surface using just the ATM volatility and (presumably) the Greeks?

Your help is greatly appreciated!

## Answer by Meph (score 2)

https://quant.stackexchange.com/a/59777

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.