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

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