A Modified Explicit Method for the Black-scholes Equation with Positivity Preserving Property

Volume 15, Issue 4, pp 287-293 http://dx.doi.org/10.22436/jmcs.015.04.05

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Authors

M. Mehdizadeh Khalsaraei - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran R. Shokri Jahandizi - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran

Abstract

In this paper, we show that the standard finite difference scheme can generate numerical drawbacks such as spurious oscillations in the solution of the famous Black-Scholes partial differential equation, in the presence of discontinuities. We propose a modification of this scheme based on a nonstandard discretization. The proposed scheme is free of spurious oscillations and satisfies the positivity requirement, as is demanded for the financial solution of the Black-Scholes equation.

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Keywords

• Black-Scholes equation
• Nonstandard finite differences
• Positivity preserving
• Stability.

MSC

•  65M12
•  65M06
•  35K57

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