Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

Hans U Gerber; Elias S.W Shiu; Hailiang Yang

doi:10.1016/j.insmatheco.2015.06.006

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Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

Journal article

Peer reviewed

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

Hans U Gerber, Elias S.W Shiu and Hailiang Yang

Insurance, mathematics & economics, Vol.64, pp.313-325

09/2015

DOI: 10.1016/j.insmatheco.2015.06.006

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Abstract

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener–Hopf factorization. •Wiener–Hopf factorization for geometrically stopped random walks is derived.•Curtate-future-lifetime is approximated by combinations of geometric distributions.•The logarithm of the stock price process is modeled as a binomial or trinomial tree.•Closed-form formulas for various equity-linked death benefits are derived.

IM10

IM40

Equity-linked death benefits

IE50

Random walk

Geometric stopping

Esscher transform

IB10

Binomial and trinomial tree models

Details

Title: Subtitle: Geometric stopping of a random walk and its applications to valuing equity-linked death benefits
Creators: Hans U Gerber - Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Elias S.W Shiu - Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242-1409, USA
Hailiang Yang - Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Resource Type: Journal article
Publication Details: Insurance, mathematics & economics, Vol.64, pp.313-325
DOI: 10.1016/j.insmatheco.2015.06.006
ISSN: 0167-6687
eISSN: 1873-5959
Publisher: Elsevier B.V
Grant note: name: Research Grants Council of the Hong Kong Special Administrative Region, award: HKU 705313P; name: Society of Actuaries’ Centers of Actuarial Excellence Research Grants
Language: English
Date published: 09/2015
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9983985854902771

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