Explicit Discretization Programming Approach to Capital Asset Pricing Model

Abstract

When estimating higher-order derivatives of a partial differential equation, it is often essential to compute approximations for artificial boundaries. In this paper we formulate an explicit discretization model for approximation of beta-coefficient of Capital Asset Pricing Model (CAPM). The method calculates higher-order derivatives for beta-coefficient function using discrete data points. Using Cartesian Laplacian Operator the paper estimates higher-order beta approximation for non-uniform multi-dimensional discretization. The method underlying partial differential equation is stated consistent with both uniform and non-uniform grid points as represented by the linearized scheme in both single and multi-dimensional discretization of systematic risk within the CAPM framework.