Pricing Multi-asset Equity Options Driven by a Multidimensional Variance Gamma Process Under Nonlinear Dependence Structures

In finance, dependence structure between assets is of great importance. For example, pricing options involving many assets, one must make preassumption about the dependence structure between assets or one important issue in risk management is to find out the dependence structure when calculating VaR. The aim of this paper is to explore the dynamic properties of a multidimensional Variance Gamma process, which has non Gaussian marginal features and non linear dependence structure. We use copula functions to specify the dependence structure of underlying assets. We study the effect of different choices for the dependence functions to the prices of a set of multi-asset equity options. The analysis is conducted using 5-dimensional baskets that consist of Jakarta Stock Exchange Composite Index (IHSG) and four other Asian Indices, Hang Seng, Nikkei, KOSPI, Straits Times Index (STI) and a standard payoff functions for multi-asset options. The results show that the different choices of dependence structure do not give significantly different option prices.