A reliable numerical method to price arithmetic Asian options

We design and analyze two numerical methods for pricing Asian options. The first one is an explicit finite difference method and therefore, as usual, only conditionally stable. The second method is an implicit finite difference method and unconditionally stable. To explore the basic ideas of analysis, we discuss the explicit method in detail and then highlight the crucial steps in the analysis of the implicit method. Numerical results obtained by these two methods are compared with those obtained by an improved Monte Carlo method. The proposed implicit method is very robust as is evident from the comparative numerical results. We also provide additional numerical results that confirm theoretical investigations done by many other researchers.