Finite Difference Method for the Multi-Asset Black–Scholes Equations

Sangkwon Kim, Darae Jeong, Chaeyoung Lee and Junseok Kim
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Sangkwon Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Darae Jeong: Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea
Chaeyoung Lee: Department of Mathematics, Korea University, Seoul 02841, Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Korea

Mathematics, 2020, vol. 8, issue 3, 1-17

Abstract: In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

Keywords: operator splitting method; Black–Scholes equations; option pricing; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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