Super-replication of life-contingent options under the Black–Scholes framework

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2024-04-05 DOI:10.1017/jpr.2024.10

Ze-An Ng, You-Beng Koh, Tee-How Loo, Hailiang Yang

引用次数: 0

Abstract

We consider the super-replication problem for a class of exotic options known as life-contingent options within the framework of the Black–Scholes market model. The option is allowed to be exercised if the death of the option holder occurs before the expiry date, otherwise there is a compensation payoff at the expiry date. We show that there exists a minimal super-replication portfolio and determine the associated initial investment. We then give a characterisation of when replication of the option is possible. Finally, we give an example of an explicit super-replicating hedge for a simple life-contingent option.

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布莱克-斯科尔斯（Black-Scholes）框架下终身期权的超级复制

我们在布莱克-斯科尔斯（Black-Scholes）市场模型的框架内考虑了一类特殊期权的超级复制问题，这类期权被称为生命条件期权。如果期权持有者在到期日之前死亡，期权可以被行使，否则在到期日会有补偿性报酬。我们证明存在一个最小的超级复制投资组合，并确定了相关的初始投资。然后，我们给出了期权复制何时可能的特征。最后，我们举例说明了一个简单的生命相关期权的显式超级复制对冲。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.