TY - JOUR
T1 - A practical finite difference method for the three-dimensional Black-Scholes equation
AU - Kim, Junseok
AU - Kim, Taekkeun
AU - Jo, Jaehyun
AU - Choi, Yongho
AU - Lee, Seunggyu
AU - Hwang, Hyeongseok
AU - Yoo, Minhyun
AU - Jeong, Darae
N1 - Funding Information:
The first author (J.S. Kim) was supported by a subproject of project Research for Applications of Mathematical Principles (No C21501) and supported by the National Institute of Mathematics Sciences (NIMS) . The corresponding author (D. Jeong) was supported by a Korea University Grant. The authors are grateful to the anonymous referees whose valuable suggestions and comments significantly improved the quality of this paper.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - 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.
AB - 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.
KW - Black-Scholes partial differential equation
KW - Equity-linked securities
KW - Non-uniform grid
KW - Operator splitting method
KW - Option pricing
UR - http://www.scopus.com/inward/record.url?scp=84960338682&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2015.12.012
DO - 10.1016/j.ejor.2015.12.012
M3 - Article
AN - SCOPUS:84960338682
SN - 0377-2217
VL - 252
SP - 183
EP - 190
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -