Operator Splitting Method to Solve the Linear Complementarity Problem for Pricing American Option: An Approximation of Error

In this manuscript, we proposed the stability and error analysis for the backward difference operator splitting (BDF-OS) methods to solve the linear complementarity problem (LCP) for pricing the American option under the Black-Scholes framework. The OS schemes have been successfully applied to a variety of Black-Scholes models. It is easy to apply on LCP because the complementarity conditions and the differential equation are segregated and examined separately. We provided an error estimate for these methods and the priori stability estimates for operator splitting strategies based on the BDF1 and BDF2 approaches. We performed numerical experiments and illustrated the order and efficiency of the BDF1 and BDF2 approaches for the test problems to emphasize the convergence behavior of the proposed methods. We have also verified the numerical results with the existing methods in the literature.