Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk

TL;DR

This paper introduces a novel combination of randomized quasi-Monte Carlo methods with importance sampling techniques to improve the robustness and efficiency of risk estimation in portfolio market risk simulations.

Contribution

It is the first to integrate randomized quasi-Monte Carlo with variance reduction techniques for portfolio risk assessment under the t-copula model.

Findings

Enhanced robustness of risk estimates with quasi-Monte Carlo sequences.

Improved efficiency in simulating loss probabilities and excesses.

Effective reduction of variance in numerical results.

Abstract

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no paper discussing combining the randomized quasi-Monte Carlo method with variance reduction techniques. In this paper, we combine the randomized quasi-Monte Carlo method with importance sampling and stratified importance sampling. Numerical results for realistic portfolio examples suggest that replacing pseudorandom numbers (Monte Carlo) with quasi-random sequences (quasi-Monte Carlo) in the simulations increases the robustness of the estimates once we reduce the effective dimension and the non-smoothness of the integrands.