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

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

2003-09-17

arxiv.org/abs/math/0309276v1

Mathematics

Numerical Analysis

Scientific paper

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.

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