Long-time trajectorial large deviations for affine stochastic volatility models and application to variance reduction for option pricing

TL;DR

This paper extends variance reduction techniques for derivative pricing to affine stochastic volatility models, proving a large deviations principle and applying a time-dependent Esscher transform to improve Monte Carlo efficiency.

Contribution

It introduces a large deviations framework for affine stochastic volatility models and adapts variance reduction via a time-dependent Esscher transform for improved option pricing.

Findings

Effective variance reduction in Heston models demonstrated

Numerical efficiency shown for models with and without jumps

Theoretical large deviations principle established for affine models

Abstract

This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential L\'evy models, to affine stochastic volatility models (Keller-Ressel, 2011). We begin by proving a pathwise large deviations principle for affine stochastic volatility models. We then apply a time-dependent Esscher transform to the affine process and use Varadhan's lemma, in the fashion of (Guasoni and Robertson, 2008) and (Robertson, 2010), to approximate the problem of finding the Esscher measure that minimises the variance of the Monte-Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate the numerical efficiency of the method.