Discretizing the Information Based Asset Price Dynamics

Abstract

The dynamics of the asset process and variance process are driven by continuous time processes in the Information Based Asset Pricing Framework as proposed by Brody, Hughson and Macrina, also known as the BHM Model. To make use of numerical simulation, the continuous time processes can be discretized to discrete time processes. Here, two discretization schemes will be looked at: Euler scheme and Milstein scheme. The main objective of this study is to apply the two discretization schemes to the Information Based Asset Picing Framework. The two schemes will first be applied to the Black-Scholes and the Heston models and then extended to the BHM model. Studies have shown that the Euler scheme approach to discretization can be inefficient which makes the use of the Milstein scheme approach to discretization more accurate due to the expansion of the coefficients involved in the stochastic differential equation.