Backfilling Missing Option Quotes by Interpolating Implied Volatility
Summary
The document considers filling missing market-maker bid and ask values across strikes and maturities when historical option prices are available for all liquid contracts and fair quotes exist for only some. It covers both European options, for which the researcher proposes Black–Scholes, and American options, for which a binomial model is proposed. A practical constraint is missing contemporaneous inputs such as rates and dividend yields.
The suggested starting point is to convert observed option prices into implied volatilities, interpolate the gaps in that representation, then convert the estimates back into prices. Consistent, reasonable assumptions for unavailable inputs may limit the effect of those assumptions, but this needs testing. The response points to methods for filling gaps using related time series as a possible starting point; irregularly missing quotes make estimating relationships between historical and market-maker data more involved. It offers no validated interpolation procedure or empirical results, so the proposed workflow remains a research approach to test.
Key ideas
- Convert observed option prices to implied volatility before attempting to fill missing fair quotes.
- Interpolate missing values in implied volatility, then convert them back into prices using consistent model assumptions.
- Unavailable rates and dividend yields require assumptions that should be tested for their effect.
- Irregular gaps complicate the use of relationships between historical prices and market-maker quotes.
- The suggested approach is a starting point, not a demonstrated or validated calibration method.
Tags
Full text
# How to 'calibrate' simple pricing models for equity index options and equity options? # How to 'calibrate' simple pricing models for equity index options and equity options? I am interested in doing some research on plain vanilla equity options and equity index options. I have historical data for these options. I also happen to have market maker 'fair price' (bid and ask) for SOME strikes for these options. I want to 'backfill' the missing 'fair prices' for the strikes for which there is no data. There are two exercise types for the options data I have - US and Euro(pean). For the Euro style options, I will be using a simple BS model, for the US style options, I will be using a Binomial model. To summarize, this is what I have: - Historical bid/ask prices for all (liquid) strikes and maturities - MM 'fair value' bid/ask values for SOME of the available strikes and maturities What I want/need MM 'fair value' bid/ask values accross ALL of the available strikes and maturities My question is this: Given the data that I have, how can I best 'backfill' the missing 'fair value' bid/ask prices?, so that I have 'fair value' bid/ask prices for all strikes and maturities. A practical note worth pointing out: I can estimate historical volatility of the underlying if need be (for the BSM), but I will not have access to prevailing rates, dividend yields (and all the other 'niceties' required by some models). ## Answer by Tal Fishman (score 2, accepted) https://quant.stackexchange.com/a/2699 The starting point for your analysis should be to convert all your options bid/ask prices to implied volatilities, which are the invariant (time-homogeneous, i.i.d.) process in your case. Even though you do not have the dividend yield and other factors necessary to back out the implied volatility, so long as you use the same assumptions (and they are reasonable assumptions) when converting back from your interpolated implied volatilities to prices, it should not greatly affect the results. However, you should test this assumption. Once you've done that, your case is highly relevant and similar to one I asked about recently: > How to interpolate gaps in a time series using closely related time series? Note: I actually have not (yet) been able to attempt to apply some of the methods mentioned in that post, but they at least sound like some reasonable starting points. Your case may differ slightly in that the gaps occur irregularly, making a calculation of the covariance between "historical" and "market maker" quotes more involved (but still not impossible).
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