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Optimal importance sampling for L\'evy Processes

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  • Adrien Genin
  • Peter Tankov

Abstract

We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Using recent results from the theory of large deviations on the path space for processes with independent increments, we compute an explicit asymptotic approximation for the variance of the pay-off under an Esscher-style change of measure. Minimizing this asymptotic variance using convex duality, we then obtain an easy to compite asymptotically efficient importance sampling estimator of the option price. Numerical tests for European baskets and for Asian options in the variance gamma model show consistent variance reduction with a very small computational overhead.

Suggested Citation

  • Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    • Handle: RePEc:arx:papers:1608.04621
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    References listed on IDEAS

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    Cited by:

    1. Zorana Grbac & David Krief & Peter Tankov, 2018. "Long-time trajectorial large deviations for affine stochastic volatility models and application to variance reduction for option pricing," Papers 1809.06153, arXiv.org.
    2. Aur'elien Alfonsi & David Krief & Peter Tankov, 2018. "Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing," Papers 1806.06883, arXiv.org.

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