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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?

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See how the VIX is calculated from S&P options here: cboe.com/micro/vix/VIXoptionsFAQ.aspx. –  Peter Irojah Apr 9 '12 at 14:59
Also Check out Kinetics EOD: kinetick.com/end-of-day and I think but not tried for options, one can get data from yahoo via Matlab. –  Peter Irojah Apr 9 '12 at 15:07
Found a similar thread: quant.stackexchange.com/questions/3144/… –  Peter Irojah Apr 9 '12 at 17:40
Peter: See first sentence of my question... –  vonjd Apr 9 '12 at 18:27
Lol, how'd I miss that, :-) –  Peter Irojah Apr 9 '12 at 18:30
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2 Answers

up vote 4 down vote accepted

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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Thank you - the answer is that historical option prices are very expensive - or do you have a good source? –  vonjd Apr 9 '12 at 8:26
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Volatility is one of the inputs in the original Black-Scholes formula. If the VIX index tells you much on the volatility to plug into your pricer for the estimation of the value of the options on the S&P500. Good for you!

Now, one has to recall that Black-Scholes world assumes log-normality of the underlying as well as constant volatility. From that, it is clear you have to resort on an extended version of the original Black-Scholes framework for the corrections you wish.

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So what exactly is the extended version of the Black-Scholes framework that you recommend? @vonjd is asking about the effects of the volatility smile when backtesting against historical CBOE data. –  chrisaycock Apr 8 '12 at 14:30
chrisaycock is right: this is just kind of rephrasing my question :-( –  vonjd Apr 8 '12 at 14:37
Hello Chrisaycock. Do you know the paper Performance of VIX Option Pricing Models: Empirical Evidence Beyond Simulation? –  edouard Apr 8 '12 at 14:39
Can you summarize the contents of that paper in reference to @vonjd's question? Merely posting a link with no explanation doesn't help anyone. –  chrisaycock Apr 8 '12 at 16:15
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