A practical finite difference method for the three-dimensional Black-Scholes equation

Junseok Kim, Taekkeun Kim, Jaehyun Jo, Yongho Choi, Seunggyu Lee, Hyeongseok Hwang, Minhyun Yoo, Darae Jeong

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


In this paper, we develop a fast and accurate numerical method for pricing of the three-asset equity-linked securities options. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a non-uniform finite difference method and the resulting discrete equations are solved by using an operator splitting method. For fast and accurate calculation, we put more grid points near the singularity of the nonsmooth payoff function. To demonstrate the accuracy and efficiency of the proposed numerical method, we compare the results of the method with those from Monte Carlo simulation in terms of computational cost and accuracy. The numerical results show that the cost of the proposed method is comparable to that of the Monte Carlo simulation and it provides more stable hedging parameters such as the Greeks.

Original languageEnglish
Pages (from-to)183-190
Number of pages8
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 2016 Jul 1

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.


  • Black-Scholes partial differential equation
  • Equity-linked securities
  • Non-uniform grid
  • Operator splitting method
  • Option pricing

ASJC Scopus subject areas

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


Dive into the research topics of 'A practical finite difference method for the three-dimensional Black-Scholes equation'. Together they form a unique fingerprint.

Cite this