Exact retrospective Monte Carlo computation of arithmetic average Asian options

Benjamin Jourdain (1) , Mohamed Sbai (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average Asian options in the Black and 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.

Mots clés: Exact simulation; Monte Carlo; Asian options

Domaines: Probabilités [math.PR]

Benjamin Jourdain, Mohamed Sbai. Exact retrospective Monte Carlo computation of arithmetic average Asian options. Monte Carlo Methods and Applications, 2007, 13 (2), pp 135-171. ⟨10.1515/mcma.2007.008⟩. ⟨hal-00141141v4⟩