Least Squares Importance Sampling for Libor Market Models

TL;DR

This paper introduces Least Squares Importance Sampling (LSIS), a method that optimizes sampling distributions in Monte Carlo simulations of Libor Market Models, significantly reducing variance and increasing computational efficiency.

Contribution

The paper presents a novel LSIS approach that automatically optimizes sampling distributions in Libor Market Model simulations, enhancing efficiency over traditional methods.

Findings

LSIS significantly reduces Monte Carlo estimator variance.

Combining LSIS with stratified sampling yields large speed-ups.

Numerical examples demonstrate LSIS's effectiveness in practice.

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.