An Alternating-Direction Implicit Difference Scheme for Pricing Asian Options

We propose a fast and stable numerical method to evaluate two-dimensional partial differential equation (PDE) for pricing arithmetic average Asian options. The numerical method is deduced by combining an alternating-direction technique and the central difference scheme on a piecewise uniform mesh. The numerical scheme is stable in the maximum norm, which is true for arbitrary volatility and arbitrary interest rate. It is proved that the scheme is second-order convergent with respect to the asset price. Numerical results support the theoretical results.