TY - JOUR
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.
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
UR - http://www.scopus.com/inward/record.url?scp=85082405628&partnerID=8YFLogxK
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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 -