Multivariate Integral Perturbation Techniques - I (Theory)

Details Multivariate Integral Perturbation Techniques - I (Theory) Multivariate Integral Perturbation Techniques - I (Theory)

2006-11-14

arxiv.org/abs/cs/0611061v1

Computer Science

Computational Engineering, Finance, and Science

25 pages, 2 figures

Scientific paper

We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This perturbative idea can also be applied to multivariate Student-t integrals. We evaluate the perturbation expansion explicitly through 2nd order, and discuss the convergence, including enhancement using Pade approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities.

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