Efficient Black-Box Importance Sampling for VaR and CVaR Estimation

TL;DR

This paper introduces an efficient black-box importance sampling method for accurately estimating tail risks like VaR and CVaR in complex loss models, automating the change-of-measure process for optimal variance reduction.

Contribution

It proposes a self-structuring importance sampling algorithm that learns the concentration properties of the loss distribution without prior knowledge, improving tail risk estimation.

Findings

Achieves asymptotically optimal variance reduction.

Demonstrates effectiveness through simulation experiments.

Applicable to complex, black-box loss functions.

Abstract

This paper considers Importance Sampling (IS) for the estimation of tail risks of a loss defined in terms of a sophisticated object such as a machine learning feature map or a mixed integer linear optimisation formulation. Assuming only black-box access to the loss and the distribution of the underlying random vector, the paper presents an efficient IS algorithm for estimating the Value at Risk and Conditional Value at Risk. The key challenge in any IS procedure, namely, identifying an appropriate change-of-measure, is automated with a self-structuring IS transformation that learns and replicates the concentration properties of the conditional excess from less rare samples. The resulting estimators enjoy asymptotically optimal variance reduction when viewed in the logarithmic scale. Simulation experiments highlight the efficacy and practicality of the proposed scheme