Large and moderate deviations for importance sampling in the Heston model

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.