Mathematics (Mar 2020)

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

  • Sangkwon Kim,
  • Darae Jeong,
  • Chaeyoung Lee,
  • Junseok Kim

DOI
https://doi.org/10.3390/math8030391
Journal volume & issue
Vol. 8, no. 3
p. 391

Abstract

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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