Pricing CAC 40 Index Options with Stochastic Volatility

This paper fulfills the lack of option pricing empirical studies devoted to the French market and is also the first paper that brings a comparison between the Heston (1993) closed-form solution model and the Hull and White (1988) model, built in a series expansion form. The empirical study is carried out on French PXL European call options written on the CAC 40 index during the first half of 2001. We discuss calibration 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 decreasing with maturity and low strike prices. We found that both models offered comparable pricing performance except for the short-term contracts and deep-out-the-money calls where the Hull and White (1988) model failed much more that the Heston (1993) model. To fit the implied volatility dynamic, the Heston (1993) model allows smile patterns to transform into skew patterns while the Hull and White (1988) model allows only for changes in the skew slope sign. However, we show that this is linked with the values of the structural parameters.