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Likelihood ratio gradient estimation for Meixner distribution and Lévy processes

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  • Reiichiro Kawai

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Abstract

We address the problem of gradient estimation with respect to four characterizing parameters of the Meixner distribution and Lévy process. With the help of the explicit marginal probability density function, the likelihood ratio method is directly applicable, while unbiased estimators may contain infinite random series in their score function. We quantify the estimator bias arising when the infinite series is truncated to finite term. We further propose a substantially simple exact simulation method for the Meixner distribution, based on acceptance-rejection sampling and the Esscher density transform. Numerical results are presented in the context of financial Greeks to illustrate the effectiveness of our formulas along with bias estimates. Copyright Springer-Verlag 2012

Suggested Citation

  • Reiichiro Kawai, 2012. "Likelihood ratio gradient estimation for Meixner distribution and Lévy processes," Computational Statistics, Springer, vol. 27(4), pages 739-755, December.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:739-755 DOI: 10.1007/s00180-011-0288-7
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    References listed on IDEAS

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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, May.
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    Cited by:

    1. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
    2. D. J. Manuge, 2015. "L\'evy Processes For Finance: An Introduction In R," Papers 1503.03902, arXiv.org.

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