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Exact retrospective Monte Carlo computation of arithmetic average Asian options


  • Jourdain Benjamin


  • Sbai Mohamed

    () (6-8 av. Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. Email:)


Taking advantage of the recent literature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts [A. Beskos, O. Papaspiliopoulos, and Gareth O. Roberts, Retrospective exact simulation of diffusion sample paths. Bernoulli 12 (December 2006).]) and unbiased estimation of the expectation of certain functional integrals (Wagner [W. Wagner, Unbiased Monte Carlo evaluation of certain functional integrals. J. Comput. Phys. 71 (1987), 21–33.], Beskos et al. [A. Beskos, O. Papaspiliopoulos,Gareth O. Roberts, and P. Fearnhead, Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. To appear in the Journal of the Royal Statistical Society, Series B.] and Fearnhead et al. [P. Fearnhead, O. Papaspiliopoulos, and G. O. Roberts, Particle Filters for Partially observed diffusions. Working paper: Lancaster University. (2006).]), we apply an exact simulation based technique for pricing continuous arithmetic average Asian options in the Black & Scholes framework. Unlike existing Monte Carlo methods, we are no longer prone to the discretization bias resulting from the approximation of continuous time processes through discrete sampling. Numerical results of simulation studies are presented and variance reduction problems are considered.

Suggested Citation

  • Jourdain Benjamin & Sbai Mohamed, 2007. "Exact retrospective Monte Carlo computation of arithmetic average Asian options," Monte Carlo Methods and Applications, De Gruyter, vol. 13(2), pages 135-171, July.
  • Handle: RePEc:bpj:mcmeap:v:13:y:2007:i:2:p:135-171:n:3

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    References listed on IDEAS

    1. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    4. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    5. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    6. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777.
    7. Tina Hviid Rydberg, 1997. "A note on the existence of unique equivalent martingale measures in a Markovian setting," Finance and Stochastics, Springer, vol. 1(3), pages 251-257.
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