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Finite Difference Method for the Multi-Asset Black-Scholes Equations
- Authors
- Kim, Sangkwon; Jeong, Darae; Lee, Chaeyoung; Kim, Junseok
- Issue Date
- 3월-2020
- Publisher
- MDPI
- Keywords
- operator splitting method; Black-Scholes equations; option pricing; finite difference method
- Citation
- MATHEMATICS, v.8, no.3
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICS
- Volume
- 8
- Number
- 3
- ISSN
- 2227-7390
- 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.
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