TY - JOUR
T1 - Hybrid Laplace transform and finite difference methods for pricing American options under complex models
AU - Ma, Jingtang
AU - Zhou, Zhiqiang
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/8/1
Y1 - 2017/8/1
N2 - In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.
AB - In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.
KW - American option pricing
KW - Finite difference methods
KW - Fractional partial differential equations
KW - Laplace transform methods
KW - Partial differential equations
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U2 - 10.1016/j.camwa.2017.04.018
DO - 10.1016/j.camwa.2017.04.018
M3 - Article
AN - SCOPUS:85020887117
SN - 0898-1221
VL - 74
SP - 369
EP - 384
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 3
ER -