Error estimates for lagrange-galerkin approximation of American options valuation

Abstract

© 2020 Society for Industrial and Applied Mathematics. The Lagrange-Galerkin scheme is studied for degenerate parabolic variational inequality arising in connection with the pricing of American options. This scheme is constructed using a combination of characteristic method for approximating the material derivative and the finite element method for approximating the diffiusion part of the equation. The accuracy of the constructed discrete scheme is established by comparing it with the known implicit time stepping (backward Euler) finite element scheme. An error estimate of O(h + τ3=4) in the energy norm of the differential operator of the problem is obtained, where h and τ denote the mesh parameters in space and time, respectively. The results of numerical calculations presented in the article for some American call options problems indicate the optimality of the theoretical error estimate.