Approximation of Multiple Integrals over Hyperboloids with Application to a Quadratic Portfolio with Options

Jules Sadefo Kamdem and Alan Genz

Papers from arXiv.org

Abstract: We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid integrals to a product of two radial integrals and two spherical surface integrals. Numerical approximation methods for the transformed integrals are constructed. The application of these methods is demonstrated using some financial applications examples.

Date: 2003-09
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Related works:
Journal Article: Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options (2008)
Working Paper: Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options (2008)
Working Paper: Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options (2008)
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