In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. 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 such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

Multivariate modeling of dependence and its impact on risk assessment remains a major concern for financial institutions. Thus, the copula model, in particular Archimedean hierarchical copulas (HAC) appears as a promising alternative, capable to precisely capture the structure of dependence between financial variables. This study aims to widen the sphere of practical applicability of the HAC model combined with the ARMA-APARCH volatility forecast model and the extreme values theory (EVT). A sequential process of modeling of the VaR of a portfolio based on the ARMA-APARCH-EVT-HAC model is discussed. The empirical analysis conducted with data from international stock market indices clearly illustrates the performance and accuracy of modeling based on HACs.