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Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model

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  • Athanassios N. Avramidis

    ()
    (Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada)

  • Pierre L'Ecuyer

    ()
    (Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada)

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    Abstract

    We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoffs, we obtain a pair of estimators (named low and high) with expectations that (1) are monotone along any such bridge sampler, and (2) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive (infinitely expensive in some situations) to compute. By using these bounds with extrapolation techniques, we obtain significant efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi-Monte Carlo to reduce the variance and thus further improve the efficiency. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.

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    File URL: http://dx.doi.org/10.1287/mnsc.1060.0575
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 52 (2006)
    Issue (Month): 12 (December)
    Pages: 1930-1944

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    Handle: RePEc:inm:ormnsc:v:52:y:2006:i:12:p:1930-1944

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    Related research

    Keywords: option pricing; efficiency improvement; extrapolation; quasi-Monte Carlo; variance gamma;

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    Cited by:
    1. Ye, Zhi-Sheng, 2013. "On the conditional increments of degradation processes," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2531-2536.
    2. Klößner, Stefan & Becker, Martin & Friedmann, Ralph, 2012. "Modeling and measuring intraday overreaction of stock prices," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1152-1163.
    3. 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.
    4. Madan, Dilip B. & Schoutens, Wim, 2013. "Systemic risk tradeoffs and option prices," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 222-230.

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