Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem

摘要

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options.We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.