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Deep Importance Sampling

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  • Benjamin Virrion

    (CEREMADE)

Abstract

We present a generic path-dependent importance sampling algorithm where the Girsanov induced change of probability on the path space is represented by a sequence of neural networks taking the past of the trajectory as an input. At each learning step, the neural networks' parameters are trained so as to reduce the variance of the Monte Carlo estimator induced by this change of measure. This allows for a generic path dependent change of measure which can be used to reduce the variance of any path-dependent financial payoff. We show in our numerical experiments that for payoffs consisting of either a call, an asymmetric combination of calls and puts, a symmetric combination of calls and puts, a multi coupon autocall or a single coupon autocall, we are able to reduce the variance of the Monte Carlo estimators by factors between 2 and 9. The numerical experiments also show that the method is very robust to changes in the parameter values, which means that in practice, the training can be done offline and only updated on a weekly basis.

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  • Benjamin Virrion, 2020. "Deep Importance Sampling," Papers 2007.02692, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2007.02692
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    References listed on IDEAS

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    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    3. Benjamin Virrion, 2020. "Deep Importance Sampling," Working Papers hal-02887331, HAL.
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    Cited by:

    1. Benjamin Virrion, 2020. "Deep Importance Sampling," Working Papers hal-02887331, HAL.

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