Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options

Authors:
J. Sadefo Kamdem;A. Genz
Affiliations:
Laboratoire de Mathématiques, CNRS UMR 6056, BP 1039 Moulin de la housse 51687 Reims cedex 2, France;Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

An application involving a financial quadratic portfolio, where the joint underlying log-returns follow a multivariate elliptic distribution, is considered. This motivates the need for methods for the approximation of multiple integrals over hyperboloids. Transformations are used to reduce the hyperboloid integrals to products of integrals which can be approximated with appropriate numerical methods. The application of these methods is demonstrated using some financial applications examples.