Pricing Cac 40 Index Options with Stochastic Volatility

The failure of the Black-Scholes (1973) model is now well documented in the literature. In this article, we discuss two alternative option valuation models whose volatility follows a stochastic process. Namely, the Heston (1993) closed-form solution model and the Hull and White (1988) model in a series expansion form, both allowing for arbitrary correlation between increments. The empirical study is carried out on French PXL European call options written on the CAC 40 index during the first half of year 2001. This paper fulfills the lack of option pricing empirical studies devoted to the French market. We discuss calibration of the models and results obtained from the out-of-sample pricing using analysis in cross-section. We also discuss the empirical dynamic of the skew. We found that misprising was globally deacreasing with maturity and increasing with low strike prices. We find that the Heston (1993) model was more likely to capture the changes in the implied volatility regime in that it can allows smile patterns to transform into skew patterns while the Hull and White (1988) model allows only for changes in the skew slope sign. We explain to what extent this phenomenon is linked with the values of some of the structural parameters