The valuation of multivariate equity options by means of copulas: Theory and application to the European derivatives market

Abstract

This article 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 that 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 that best fits the observed dependence structure. In addition, based on price data from single underlying options traded at the European Exchange (Eurex) 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. © 2011 Macmillan Publishers Ltd.