Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models. (March 2021)

• Record Type: Journal Article
• Authors: Grbac, Zorana; Krief, David; Tankov, Peter
• Is Part Of: Advances in applied probability. Volume 53:Number 1(2021)
• Page Start: 220
• Page End: 250
• Publication Date: 2021-03
• Subjects: Large deviations, -- Monte Carlo methods, -- importance sampling, -- affine stochastic volatility; 60F10, -- 91G60; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2020.58
• Languages: English
• ISSNs: 0001-8678

Abstract

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.