Table of Contents
Journal of Probability
Volume 2014, Article ID 839204, 11 pages
http://dx.doi.org/10.1155/2014/839204
Research Article

Multivariate Option Pricing with Pair-Copulas

1Group Strategic Planning and Control at Generali, Head Office, Via N. Machiavelli 4, 34132 Trieste, Italy
2Department of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, Italy

Received 31 July 2014; Accepted 9 December 2014; Published 25 December 2014

Academic Editor: Edward Furman

Copyright © 2014 Anna Barban and Luca Di Persio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.