The performance of popular stochastic volatility option pricing models during the subprime crisis

Abstract

Using daily options prices on the Eurostoxx 50 stock index over the whole year 2008, we compare the performance of three popular Stochastic Volatility (SV) models (Heston, 1993 Heston, S. 1993. A closed-form solution for options with stochastic volatility. Review of Financial Studies, 6: 327–44. [Crossref], [Web of Science ®] , [Google Scholar]; Bates, 1996 Bates, D. 1996. Jumps and stochastic volatility: exchange rate processes implicit in deutschemark options. Review of Financial Studies, 9: 69–107. [Crossref], [Web of Science ®] , [Google Scholar]; Heston and Nandi, 2000 Heston, S and Nandi, S. 2000. A closed-form GARCH option valuation model. Review of Financial Studies, 13: 585–625. [Crossref], [Web of Science ®] , [Google Scholar]), in addition to the traditional Black–Scholes model and a proprietary trading desk model. We show that the most consistent in-sample and out-of-sample statistical performance is obtained for the internal model. However, the Bates model seems to be better suited to Short Term (ST, out-of-the-money) options while the Heston model seems to perform better for medium or Long Term (LT) options. In terms of hedging performance, the Heston and Nandi model exhibits the best average, albeit most volatile, result and the Heston model outperforms the Black–Scholes model in terms of hedging errors, mainly for option contracts that mature in-the-money.

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