Least Squares Importance Sampling for Libor Market Models

Abstract

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of a quick presimulation algorithm of straightforward implementation. With several numerical examples we show that LSIS can be extremely effective in reducing the variance of Monte Carlo estimators often resulting, especially when combined with stratified sampling, in computational speed-ups of orders of magnitude.