Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas

Abstract

In this article, we present an approach which allows to take into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associeted options. Specifically, the marginal distribution of assets returns is modeled by a mixture of two gaussiens distributions. Moreover, we model the joint dependence structure of the returns using an extremal copula which is suitable for our financial data. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte-Carlo method is used to compute the values of some equity options: the call on maximum, the call on minimum, the digital option and the spreads option with the basket (Atos, Dassault systems).