This is a follow up question of this one.
My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes.
The following paper gives a good master plan how to backtest option strategies with the standard Black Scholes formula. If you use the publicly available implied volatility indices (like VIX) for the vol parameter the results are pretty good for ATM options:
How Students Can Backtest Madoff’s Claims by Michael J. Stutzer (2009)
Problems arise when you want to backtest strategies with (deep) ITM or OTM options.
My question is:
How can you produce even better historical option prices (for S&P 500 index options) with corrections for the smile with other publicly available data like SKEW and VVIX?
Answer
I suggest you avoid using the VIX for implied vols. Why? One has to consider that the VIX is not simply solely dependant on the dynamics on the S&P 500 anymore because the VIX can be traded via options, etc. Thus many more parameters affect the trajectory of the VIX. The VIX has to equal the ATM option vol because this is where arbitrage assumption manifest; the price of a derivative on expiry has to be equal the spot price on the same date.
Since you are back-testing, why can't you get the historical option prices and then calculate the implied vols (generate your volatility curve using inv) for your calculation?
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