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

Zorana Grbac, David Krief and Peter Tankov
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Zorana Grbac: UPCité - Université Paris Cité
David Krief: UPD7 - Université Paris Diderot - Paris 7
Peter Tankov: ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris

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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.

Keywords: large deviations Monte Carlo methods importance sampling affine stochastic volatility MSC2010: 91G60 60F10; large deviations; Monte Carlo methods; importance sampling; affine stochastic volatility (search for similar items in EconPapers)
Date: 2021-03-17
Note: View the original document on HAL open archive server: https://hal.science/hal-03899237v1
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Published in Advances in Applied Probability, 2021, 53 (1), pp.220-250. ⟨10.1017/apr.2020.58⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03899237

DOI: 10.1017/apr.2020.58

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