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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zorana Grbac & David Krief & Peter Tankov, 2021. "Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models," Post-Print hal-03899237, HAL.
    • Handle: RePEc:hal:journl:hal-03899237
    DOI: 10.1017/apr.2020.58
    Note: View the original document on HAL open archive server: https://hal.science/hal-03899237
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    References listed on IDEAS

    as
    1. Paolo Guasoni & Scott Robertson, 2008. "Optimal importance sampling with explicit formulas in continuous time," Finance and Stochastics, Springer, vol. 12(1), pages 1-19, January.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.
    Full references (including those not matched with items on IDEAS)

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