Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

Abstract

We establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

Large and moderate deviations for importance sampling in the Heston model

“…Remark. Variance reduction for affine stochastic volatility processes via importance sampling through the large-time approximation is extensively covered in [14], so we do not repeat the study and refer the reader to the aforementioned work.…”