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

Sangkwon Kim, Darae Jeong, Chaeyoung Lee, Junseok Kim

Research output: Contribution to journalReview articlepeer-review

8 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 languageEnglish
Article number391
JournalMathematics
Volume8
Issue number3
DOIs
Publication statusPublished - 2020 Mar 1

Bibliographical 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:
© 2020 by the authors.

Keywords

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

ASJC Scopus subject areas

  • General Mathematics

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