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A general control variate method for option pricing under Lévy processes

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  • Dingeç, Kemal Dinçer
  • Hörmann, Wolfgang
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    Abstract

    We present a general control variate method for simulating path dependent options under Lévy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option under geometric Brownian motion. The method is applicable for all types of Lévy processes for which the probability density function of the increments is available in closed form. Numerical experiments confirm that our method achieves considerable variance reduction for different options and Lévy processes. We present the applications of our general approach for Asian, lookback and barrier options under variance gamma, normal inverse Gaussian, generalized hyperbolic and Meixner processes.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 221 (2012)
    Issue (Month): 2 ()
    Pages: 368-377

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    Handle: RePEc:eee:ejores:v:221:y:2012:i:2:p:368-377

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Finance; Option pricing; Lévy processes; Monte Carlo simulation; Control variate; Numerical inversion;

    References

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    1. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, INFORMS, vol. 52(12), pages 1930-1944, December.
    2. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
    3. Reiichiro Kawai, 2012. "Likelihood ratio gradient estimation for Meixner distribution and Lévy processes," Computational Statistics, Springer, vol. 27(4), pages 739-755, December.
    4. Vladimir K. Kaishev & Dimitrina S. Dimitrova, 2009. "Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options," Management Science, INFORMS, INFORMS, vol. 55(3), pages 483-496, March.
    5. Nick Webber & Claudia Ribeiro, 2003. "A Monte Carlo Method for the Normal Inverse Gaussian Option Valuation Model using an Inverse Gaussian Bridge," Computing in Economics and Finance 2003 5, Society for Computational Economics.
    6. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(4), pages 325-349.
    7. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    8. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    9. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2011. "Using the continuous price as control variate for discretely monitored options," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 82(4), pages 691-704.
    10. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
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