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http://dx.doi.org/10.12941/jksiam.2019.23.019

FINITE DIFFERENCE METHOD FOR THE TWO-DIMENSIONAL BLACK-SCHOLES EQUATION WITH A HYBRID BOUNDARY CONDITION  

HEO, YOUNGJIN (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
HAN, HYUNSOO (DEPARTMENT OF FINANCIAL ENGINEERING, KOREA UNIVERSITY)
JANG, HANBYEOL (DEPARTMENT OF FINANCIAL ENGINEERING, KOREA UNIVERSITY)
CHOI, YONGHO (DEPARTMENT OF MATHEMATICS AND BIG DATA, DAEGU UNIVERSITY)
KIM, JUNSEOK (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.23, no.1, 2019 , pp. 19-30 More about this Journal
Abstract
In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.
Keywords
Option pricing; Black-Scholes equation; finite difference method; Greeks; boundary condition;
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Times Cited By KSCI : 1  (Citation Analysis)
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