Finite difference method for the multi-asset black-scholes equations

Sangkwon Kim; Darae Jeong; Chaeyoung Lee; Junseok Kim

doi:10.3390/math8030391

Finite difference method for the multi-asset black-scholes equations

Sangkwon Kim, Darae Jeong, Chaeyoung Lee, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Review article › peer-review

3 Citations (Scopus)

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.

Original language	English
Article number	391
Journal	Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.3390/math8030391
Publication status	Published - 2020 Mar 1

Keywords

Black-scholes equations
Finite difference method
Operator splitting method
Option pricing

ASJC Scopus subject areas

Mathematics(all)

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10.3390/math8030391

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title = "Finite difference method for the multi-asset black-scholes equations",

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 = "Black-scholes equations, Finite difference method, Operator splitting method, Option pricing",

author = "Sangkwon Kim and Darae Jeong and Chaeyoung Lee and Junseok Kim",

note = "Funding Information: Funding: The corresponding author (J.S. Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea. Publisher Copyright: {\textcopyright} 2020 by the authors.",

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T1 - Finite difference method for the multi-asset black-scholes equations

AU - Kim, Sangkwon

AU - Jeong, Darae

AU - Lee, Chaeyoung

AU - Kim, Junseok

N1 - Funding Information: Funding: The corresponding author (J.S. Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea. Publisher Copyright: © 2020 by the authors.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - Black-scholes equations

KW - Finite difference method

KW - Operator splitting method

KW - Option pricing

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U2 - 10.3390/math8030391

DO - 10.3390/math8030391

M3 - Review article

AN - SCOPUS:85082405628

VL - 8

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 3

M1 - 391

ER -

Finite difference method for the multi-asset black-scholes equations

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Keywords

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