Dec 6, 2012

Robustness of the Black-Scholes Model

Jared Woodard at Condor Options published an excellent post today - his thoughts on research paper by Carol Alexander et al on hedging efficiency of different models. From my experience - as someone who has worked for over 10 years in options market making these results are not surprising.

Pricing model standard deviation of PL, smaller is better. From with permission.

1 SABR model is my preferred model for pricing and hedging, although in production I used few critical adjustments to the original version.
2 BSM adjusted: in the research paper the adjustments that were made seemed to be quite ad-hoc, but in the performance adjusted BSM is (apparently) not far from SABR. I think this is because S&P has a lot of strikes and allows for a good (robust) fit of skew and kurtosis adjustments. I doubt this would work for option chains with very few strikes.
3 Normal mixture is worse than flat vol BSM, but with adjustments it was better than BSM. This one is not easy to explain. If normal mixture is worse than it is probably due to bad fit, instability of parameters, basically lack of robustness. But why did hedge adjustments improve performance? I don't know.

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