TY - JOUR
T1 - A Hybrid Monte Carlo and Finite Difference Method for Option Pricing
AU - Jeong, Darae
AU - Yoo, Minhyun
AU - Yoo, Changwoo
AU - Kim, Junseok
N1 - Funding Information:
Acknowledgements The author (D. Jeong) was supported by a Korea University Grant. The corresponding author (J. S. Kim) was supported by the Korea Institute for Advanced Study (KIAS) for supporting research on the financial pricing model using artificial intelligence. The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
PY - 2019/1/31
Y1 - 2019/1/31
N2 - We propose an accurate, efficient, and robust hybrid finite difference method, with a Monte Carlo boundary condition, for solving the Black–Scholes equations. The proposed method uses a far-field boundary value obtained from a Monte Carlo simulation, and can be applied to problems with non-linear payoffs at the boundary location. Numerical tests on power, powered, and two-asset European call option pricing problems are presented. Through these numerical simulations, we show that the proposed boundary treatment yields better accuracy and robustness than the most commonly used linear boundary condition. Furthermore, the proposed hybrid method is general, which means it can be applied to other types of option pricing problems. In particular, the proposed Monte Carlo boundary condition algorithm can be implemented easily in the code of the existing finite difference method, with a small modification.
AB - We propose an accurate, efficient, and robust hybrid finite difference method, with a Monte Carlo boundary condition, for solving the Black–Scholes equations. The proposed method uses a far-field boundary value obtained from a Monte Carlo simulation, and can be applied to problems with non-linear payoffs at the boundary location. Numerical tests on power, powered, and two-asset European call option pricing problems are presented. Through these numerical simulations, we show that the proposed boundary treatment yields better accuracy and robustness than the most commonly used linear boundary condition. Furthermore, the proposed hybrid method is general, which means it can be applied to other types of option pricing problems. In particular, the proposed Monte Carlo boundary condition algorithm can be implemented easily in the code of the existing finite difference method, with a small modification.
KW - Black–Scholes equation
KW - Boundary condition
KW - Finite difference method
KW - Monte Carlo simulation
KW - Option pricing
UR - http://www.scopus.com/inward/record.url?scp=85028598645&partnerID=8YFLogxK
U2 - 10.1007/s10614-017-9730-4
DO - 10.1007/s10614-017-9730-4
M3 - Article
AN - SCOPUS:85028598645
SN - 0927-7099
VL - 53
SP - 111
EP - 124
JO - Computational Economics
JF - Computational Economics
IS - 1
ER -