Short time asymptotics for American maximum options with a dividend-paying asset

Rui Hou; Yongqing Xu; Jinhua Fan; Yuanguo Zhu; Rui Hou; Yongqing Xu; Jinhua Fan; Yuanguo Zhu

doi:10.3934/math.2022772

AIMS Mathematics

2022, Volume 7, Issue 8: 13977-13993. doi: 10.3934/math.2022772

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Research article

Short time asymptotics for American maximum options with a dividend-paying asset

1.
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
2.
College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China

Received: 10 December 2021 Revised: 26 April 2022 Accepted: 09 May 2022 Published: 26 May 2022
MSC : 35K20, 91G20, 91G80

We investigate the asymptotic behaviors of American maximum options with dividend-paying assets near maturity. Using the exercise conditions of American options, we obtain the asymptotic forms of the two boundaries with respect to time-to-maturity. Furthermore, we derive the matched asymptotic expansion for the rescaled value function of American maximum option. The all results are provided with detailed computations and derivations. Numerical examples show that the asymptotic value function and exercise boundaries can provide an efficient alternative for the true ones, respectively.
- American option,
- minimum payoff,
- optimal exercise/free boundary,
- short time asymptotics
Citation: Rui Hou, Yongqing Xu, Jinhua Fan, Yuanguo Zhu. Short time asymptotics for American maximum options with a dividend-paying asset[J]. AIMS Mathematics, 2022, 7(8): 13977-13993. doi: 10.3934/math.2022772

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Abstract

We investigate the asymptotic behaviors of American maximum options with dividend-paying assets near maturity. Using the exercise conditions of American options, we obtain the asymptotic forms of the two boundaries with respect to time-to-maturity. Furthermore, we derive the matched asymptotic expansion for the rescaled value function of American maximum option. The all results are provided with detailed computations and derivations. Numerical examples show that the asymptotic value function and exercise boundaries can provide an efficient alternative for the true ones, respectively.

References

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