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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:

  1. Historical bid/ask prices for all (liquid) strikes and maturities
  2. 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).

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How are the market maker "fair" values different from the historical bid/ask? Where does the difference come from? Why do you suspect the historical data is not "fair"? – Tal Fishman Dec 31 '11 at 23:51
@TalFishman: The (historic) 'fair' bid/ask values differ from the (historic) actually "firm" quotes - in terms of price. For now, I am not concerned WHY there is a difference between the theoretical value and the "firm quotes" (I'll leave the academics to worry about the WHY). Regarding your last question - you may have misinterpreted my question. I have no views (one way or the other) on the historical data. All I want to do at this stage, is to be able to compute the 'missing' fair value bid/ask prices for strikes which don't have this data, using the inputs I outlined in my question. – Homunculus Reticulli Jan 2 '12 at 14:00

1 Answer

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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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Hi Tal, thanks for your feedback. I will use it as a starting point for any subsequent investigation. – Homunculus Reticulli Jan 3 '12 at 19:43

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