Analysis of Quantization Error in Financial Pricing via Finite Difference Methods

Abstract

In this paper, we study the error of a second order finite difference scheme for the one-dimensional convection-diffusion equation. We consider non-smooth initial conditions commonly encountered in financial pricing applications. For these initial conditions, we establish the explicit expression of the quantization error, which is loosely defined as the error of the numerical solution due to the placement of the point of non-smoothness on the numerical grid. Based on our analysis, we study the issue of optimal placement of such non-smoothness points on the grid, and the effect of smoothing operators on quantization errors.