A Note on Numerical Solution of a Linear Black-Scholes Model

Authors

  • Md. Kazi Salah Uddin Department of Mathematics, University of Dhaka, Dhaka-1000,
  • Mostak Ahmed Department of Mathematics, Jagannath University, Dhaka-1100,
  • Samir Kumar Bhowmilk Department of Mathematics and Statistics, College of Science, Al-Imam Muhammad Ibn Saud Islamic University, Riyadh,

DOI:

https://doi.org/10.3329/ganit.v33i0.17664

Keywords:

Black-Scholes model, call and put options, exact solution, finite difference schemes

Abstract

Black-Scholes equation is a well known partial differential equation in financial mathematics. In this article we discuss about some solution methods for the Black Scholes model with the European options (Call and Put) analytically as well as numerically. We study a weighted average method using different weights for numerical approximations. In fact, we approximate the model using a finite difference scheme in space first followed by a weighted average scheme for the time integration. Then we present the numerical results for the European Call and Put options. Finally, we investigate some linear algebra solvers to compare the superiority of the solvers.

GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 103-115

DOI: http://dx.doi.org/10.3329/ganit.v33i0.17664

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Published

2014-01-13

How to Cite

Uddin, M. K. S., Ahmed, M., & Bhowmilk, S. K. (2014). A Note on Numerical Solution of a Linear Black-Scholes Model. GANIT: Journal of Bangladesh Mathematical Society, 33, 103–115. https://doi.org/10.3329/ganit.v33i0.17664

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Articles