Journal of Finance and Economics
ISSN (Print): 2328-7284 ISSN (Online): 2328-7276 Website: http://www.sciepub.com/journal/jfe Editor-in-chief: Suman Banerjee
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Journal of Finance and Economics. 2019, 7(2), 68-74
DOI: 10.12691/jfe-7-2-4
Open AccessArticle

Discretizing the Information Based Asset Price Dynamics

Cynthia Ikamari1, 2, , Philip Ngare2 and Patrick Weke2

1Faculty of Business and Economics, Multimedia University of Kenya, Kenya

2School of Mathematics, University of Nairobi, Kenya

Pub. Date: May 05, 2019

Cite this paper:
Cynthia Ikamari, Philip Ngare and Patrick Weke. Discretizing the Information Based Asset Price Dynamics. Journal of Finance and Economics. 2019; 7(2):68-74. doi: 10.12691/jfe-7-2-4

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.

Keywords:
discretization Euler scheme Milstein scheme Black-Scholes model Hes-ton model BHM model

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