AN ADAPTIVE FINITE DIFFERENCE METHOD USING FAR-FIELD BOUNDARY CONDITIONS FOR THE BLACK-SCHOLES EQUATION

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 4, 2014, pp.1087-1100
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.4.1087

Title & Authors

AN ADAPTIVE FINITE DIFFERENCE METHOD USING FAR-FIELD BOUNDARY CONDITIONS FOR THE BLACK-SCHOLES EQUATION

Jeong, Darae; Ha, Taeyoung; Kim, Myoungnyoun; Shin, Jaemin; Yoon, In-Han; Kim, Junseok;

Jeong, Darae; Ha, Taeyoung; Kim, Myoungnyoun; Shin, Jaemin; Yoon, In-Han; Kim, Junseok;

Abstract

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

Keywords

Black-Scholes equation;finite difference method;far-field boundary conditions;adaptive grid;Peclet condition;

Language

English

Cited by

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