TY - JOUR
T1 - Pricing arithmetic Asian and Amerasian options
T2 - A diffusion operator integral expansion approach
AU - Ding, Kailin
AU - Cui, Zhenyu
AU - Yang, Xiaoguang
N1 - Publisher Copyright:
© 2022 Wiley Periodicals LLC.
PY - 2023/2
Y1 - 2023/2
N2 - In this paper, we propose a new explicit series expansion formula for the price of an arithmetic Asian option under the Black–Scholes model and Merton's jump-diffusion model. The method is based on an equivalence in law relation together with the diffusion operator integral method proposed by Heath and Platen. The method yields explicit series expansion formula for the Asian options' prices. The theoretical convergence of the expansion to the true value is established. We also consider the American Asian option (i.e., Amerasian option) and derive the corresponding expansion formula through the early exercise premium representation. Numerical results illustrate the accuracy and efficiency of the method as compared with benchmarks in the literature.
AB - In this paper, we propose a new explicit series expansion formula for the price of an arithmetic Asian option under the Black–Scholes model and Merton's jump-diffusion model. The method is based on an equivalence in law relation together with the diffusion operator integral method proposed by Heath and Platen. The method yields explicit series expansion formula for the Asian options' prices. The theoretical convergence of the expansion to the true value is established. We also consider the American Asian option (i.e., Amerasian option) and derive the corresponding expansion formula through the early exercise premium representation. Numerical results illustrate the accuracy and efficiency of the method as compared with benchmarks in the literature.
KW - American Asian options
KW - Asian option
KW - diffusion operator integral
KW - series expansion
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U2 - 10.1002/fut.22387
DO - 10.1002/fut.22387
M3 - Article
AN - SCOPUS:85142626000
SN - 0270-7314
VL - 43
SP - 217
EP - 241
JO - Journal of Futures Markets
JF - Journal of Futures Markets
IS - 2
ER -