The Valuation of Multivariate Equity Options by Means of Copulas : Theory and Application to the European Derivatives Market

This paper studies the valuation of multivariate equity options by determining the joint risk-neutral distribution of the underlying stock prices by means of copulas. In contrast to previous work which concentrates on two underlyings this study considers the general multivariate case. In particular, tri-variate and six-variate elliptical and Archimedean copula families are calibrated empirically in order to find the copula which best fits the observed dependence structure. Based additionally on price data from single underlying options traded at the Eurex (European Exchange) the valuation of typical multivariate options is compared between Black/Scholes-like and alternative copula-based valuation models. Remarkable differences and thus a high model risk become evident, accompanied by a distinct parameter sensitivity in the copula models