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

Part of: Mathematical finance Limit theorems

Published online by Cambridge University Press:  17 March 2021

Zorana Grbac ,
David Krief  and
Peter Tankov
Zorana Grbac*
Affiliation:
Université de Paris
David Krief*
Affiliation:
Université de Paris
Peter Tankov*
Affiliation:
ENSAE, Institut Polytechnique de Paris
*
*Postal address: 5 rue Thomas Mann, 75013Paris, France.
*Postal address: 5 rue Thomas Mann, 75013Paris, France.
****Postal address: 5 avenue Henry Le Chatelier, 91120Palaiseau, France. Email address: peter.tankov@ensae.fr
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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 deviationsMonte Carlo methodsimportance samplingaffine stochastic volatility

MSC classification

Primary: 60F10: Large deviations
Secondary: 91G60: Numerical methods (including Monte Carlo methods)
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 1 , March 2021 , pp. 220 - 250
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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