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Numerical Solution of a Linear Black-Scholes Model: A Comparative Overview

Abstract

Black-Scholes equation is a well-known partial differential equation in financial mathematics. In this paper we try to solve the European options (Call and Put) using different numerical methods as well as analytical methods. We approximate the model using a Finite Element Method (FEM) followed by weighted average method using different weights for numerical approximations. We present the numerical result of semidiscrete and full discrete schemes for European Call option and Put option by Finite Difference Method and Finite Element Method. We also present the difference of these two methods. Finally, we investigate some linear algebra solvers to verify the superiority of the solvers.

Md Kazi Salah Uddin, Md. Noor-A-Alam Siddiki*, Md Anowar Hossain

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