9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract

An Empirical Comparison of Alternative Stochastic Volatility Models

C. Schlag
M. Belledin

Goethe Universität, Frankfurt

We perform an empirical comparison of stochastic volatility models using data from the German index options market. The models compared are those de­ veloped by Stein and Stein [15], Heston [8], and Sch&oumlbel and Zhu [12], while the standard Black and Scholes [4] approach is used as a benchmark. The parameters of the four models are estimated implicitly from daily cross­ sections of option prices using a simulated annealing algorithm to overcome the numerical deficiencies of standard optimization routines. The main result in terms of pricing performance is that there is a clear advantage for stochastic volatility models compared to Black and Scholes both in and out of sample. Within the group of stochastic volatility models the more flexible approaches by Sch&oumlbel and Zhu [12] and Heston [8], allowing for a non­zero correlation between stock returns and volatility changes, are preferable to the restricted Stein and Stein model. In terms of hedging performance a slightly modified version of the Black and Scholes model is practically indistinguishable from the stochastic volatility models, and there is evidence that these more complex models are still misspecified.