A robust finite difference scheme for pricing American put options with Singularity-Separating method

In this paper we present a stable numerical method for the linear complementary problem arising from American put option pricing. The numerical method is based on a hybrid finite difference spatial discretization on a piecewise uniform mesh and an implicit time stepping technique. The scheme is stable for arbitrary volatility and arbitrary interest rate. We apply some tricks to derive the error estimates for the direct application of finite difference method to the linear complementary problem. We use the Singularity-Separating method to remove the singularity of the non-smooth payoff function. It is proved that the scheme is second-order convergent with respect to the spatial variable. Numerical results support the theoretical results.