TY - JOUR
T1 - LAPLACE BOUNDS APPROXIMATION FOR AMERICAN OPTIONS
AU - Ma, Jingtang
AU - Cui, Zhenyu
AU - Li, Wenyuan
N1 - Publisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - In this paper, we develop the lower-upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding capped (barrier) option with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.
AB - In this paper, we develop the lower-upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding capped (barrier) option with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.
KW - American option pricing
KW - Laplace transform
KW - early exercise boundary
KW - jump diffusions
KW - option bounds
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U2 - 10.1017/S0269964820000492
DO - 10.1017/S0269964820000492
M3 - Article
AN - SCOPUS:85095431087
SN - 0269-9648
VL - 36
SP - 514
EP - 547
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 2
ER -