Finite difference scheme with a moving mesh for pricing Asian options

摘要

In this paper we propose a stable numerical method for pricing Asian call options, which is based on a central difference scheme with a moving mesh in the spatial discretization and the Rannacher time stepping scheme in the time discretization. At each time mesh point we make a piecewise uniform mesh to discretise the space interval, which ensures that the matrix associated with the discrete operator is an M-matrix. Hence the spatial discretization scheme is maximum-norm stable for arbitrary volatility and arbitrary interest rate. We show that the scheme is second-order convergent with respect to both time and spatial variables. Numerical results support the theoretical results.