Moving mesh methods for pricing Asian options with regime switching

In this paper we study moving mesh implicit finite difference methods for pricing Asian options with regime switching. The price of Asian options with regime switching follows a system of partial differential equations (PDEs) with moving boundaries. Based on quadratic interpolation between two consecutive levels of computational solutions, the moving mesh finite difference methods are constructed to solve the resulted system of PDEs with moving boundaries. The moving mesh finite difference schemes studied in this paper include implicit Euler schemes, Rannacher schemes and Crank–Nicolson schemes. The convergence rates for these schemes are obtained. Numerical examples are provided to confirm the theoretical results.