Multivariate Integral Perturbation Techniques - I (Theory)
by Jan W. Dash of Moore Capital Management
Abstract: 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 Padé approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities.
Keywords: Multivariate, Gaussian, Student-t, perturbation, theory, Pade, credit, correlations, options.
Published in: International Journal of Theoretical and Applied Finance, Vol. 10, No. 8, (December 2007), pp. 1287-1304.