Exact retrospective Monte Carlo computation of arithmetic average Asian options

Jourdain Benjamin () and Sbai Mohamed ()
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Jourdain Benjamin: 6-8 av. Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. Email: jourdain@cermics.enpc.fr
Sbai Mohamed: 6-8 av. Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. Email: sbai@cermics.enpc.fr

Monte Carlo Methods and Applications, 2007, vol. 13, issue 2, 135-171

Abstract: 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.

Keywords: Arithmetic average Asian options; Black and Scholes framework; Poisson estimator. (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1515/mcma.2007.008

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