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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Robust adaptive variance reduction for normal random vectors

Workshop: Computational Methods with Applications in Finance, Insurance and the Life Sciences AND Stochastic Methods in Partial Differential Equations and Applications of Deterministic and Stochastic PDEs

Time: Mon, November 17, 2008, 16:20-17:10

Speaker: Benjamin Jourdain

Abstract

In financial models given by SDEs, after time-discretization,
computation of the price of an option amounts to the calculation of the
expectation of a random variable written as a function of a normal
random vector. In this talk, we discuss adaptive importance sampling and
stratified sampling techniques in this context.

Translation of the normal vector by a deterministic vector leads to a
parametric importance sampling technique. We show that the importance
sampling estimator of the price computed with the translation parameter
obtained by minimizing the Monte Carlo approximation of the variance
based on the same random drawings has an optimal asymptotic variance.

When the normal vector is stratified according to the values of its
scalar product with a direction, we show how to optimize this stratified
direction in terms of variance using the random drawings made to compute
the price.

Presentation slides (pdf, 768 KB)

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