Single-Index Importance Sampling with Stratification

TL;DR

This paper introduces a variance reduction technique combining single-index importance sampling with stratification, improving efficiency in estimating rare event probabilities in high-dimensional stochastic problems, especially in finance.

Contribution

It proposes a novel importance sampling method leveraging single-index structure and stratification, enhancing rare event simulation efficiency in complex models.

Findings

Outperforms standard methods in credit portfolio loss estimation

Effective in normal and t-copula models

Enhances quasi-Monte Carlo effectiveness

Abstract

In many stochastic problems, the output of interest depends on an input random vector mainly through a single random variable (or index) via an appropriate univariate transformation of the input. We exploit this feature by proposing an importance sampling method that makes rare events more likely by changing the distribution of the chosen index. Further variance reduction is guaranteed by combining this single-index importance sampling approach with stratified sampling. The dimension-reduction effect of single-index importance sampling also enhances the effectiveness of quasi-Monte Carlo methods. The proposed method applies to a wide range of financial or risk management problems. We demonstrate its efficiency for estimating large loss probabilities of a credit portfolio under a normal and t-copula model and show that our method outperforms the current standard for these problems.