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Quasi-Monte Carlo methods for the Kou model

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  • Baldeaux Jan

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Email: z3177364@science.unsw.edu.au)

Abstract

We firstly show how to formulate the finance problem as an integration problem so that QMC methods can be applied to it. Consequently, we introduce QMC approaches for the integration problems pertaining to the Poisson processes, compound Poisson processes and jump-diffusion processes underlying the Kou model. As opposed to increment-by-increment approaches, our approaches change the ordering of the variates in the integration problems to pack more variance into the opening dimensions. We report numerical experiments indicating that the approaches introduced achieve lower standard errors than the increment-by-increment approaches.

Suggested Citation

  • Baldeaux Jan, 2008. "Quasi-Monte Carlo methods for the Kou model," Monte Carlo Methods and Applications, De Gruyter, vol. 14(4), pages 281-302, January.
    • Handle: RePEc:bpj:mcmeap:v:14:y:2008:i:4:p:281-302:n:1
    DOI: 10.1515/MCMA.2008.012
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, vol. 52(12), pages 1930-1944, December.
    3. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    4. Larcher Gerhard & Predota Martin & Tichy Robert F., 2003. "Arithmetic average options in the hyperbolic model," Monte Carlo Methods and Applications, De Gruyter, vol. 9(3), pages 227-239, September.
    5. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
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    Cited by:

    1. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carlo methods for the Heston model," Papers 1202.3217, arXiv.org, revised May 2012.

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