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

Part of: Mathematical finance Stochastic analysis

Published online by Cambridge University Press:  05 April 2024

Ze-An Ng ,
You-Beng Koh Open the ORCID record for You-Beng Koh [Opens in a new window] ,
Tee-How Loo  and
Hailiang Yang
Ze-An Ng*
Affiliation:
Universiti Malaya
You-Beng Koh*
Affiliation:
Universiti Malaya
Tee-How Loo*
Affiliation:
Universiti Malaya
Hailiang Yang*
Affiliation:
Xi’an Jiaotong-Liverpool University
*
*Postal address: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603, Kuala Lumpur, Malaysia.
*Postal address: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603, Kuala Lumpur, Malaysia.
*Postal address: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603, Kuala Lumpur, Malaysia.
*****Postal address: Department of Financial and Actuarial Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, China. Email: hailiang.yang@xjtlu.edu.cn
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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.

Keywords

Exotic optionsoption pricingoption hedgingstochastic analysis

MSC classification

Primary: 91G20: Derivative securities
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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