Multivariate Option Pricing with Pair-Copulas

We propose a copula-based approach to solve the option pricing problem in the risk-neutral setting and with respect to a structured derivative written on several underlying assets. Our analysis generalizes similar results already present in the literature but limited to the trivariate case. The main difficulty of such a generalization consists in selecting the appropriate vine structure which turns to be of D-vine type, contrary to what happens in the trivariate setting where the canonical vine is sufficient. We first define the general procedure for multivariate options and then we will give a concrete example for the case of an option written on four indexes of stocks, namely, the S&P 500 Index, the Nasdaq 100 Index, the Nasdaq Composite Index, and the Nyse Composite Index. Moreover, we calibrate the proposed model, also providing a comparison analysis between real prices and simulated data to show the goodness of obtained estimates. We underline that our pair-copula decomposition method produces excellent numerical results, without restrictive assumptions on the assets dynamics or on their dependence structure, so that our copula-based approach can be used to model heterogeneous dependence structure existing between market assets of interest in a rigorous and effective way.