Large and moderate deviations for importance sampling in the Heston model

TL;DR

This paper develops a comprehensive importance sampling framework for variance reduction in stochastic volatility models, especially the Heston model, using large and moderate deviations theory, and validates it with numerical experiments.

Contribution

It introduces a novel importance sampling approach based on large and moderate deviations for the Heston model, providing explicit solutions and practical implementation guidance.

Findings

Significant variance reduction achieved in numerical tests.

Closed-form solutions facilitate easy implementation.

Theoretical analysis confirms effectiveness of the method.

Abstract

We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time, small-noise. Specialising the results to the Heston model, we derive many closed-form solutions, making the whole approach easy to implement. We support our theoretical results with a detailed numerical analysis of the variance reduction gains.