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 and Economics, 2015, vol. 64, issue C, 313-325

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.

Keywords: IM10; IE50; IM40; IB10; Equity-linked death benefits; Binomial and trinomial tree models; Random walk; Geometric stopping; Esscher transform (search for similar items in EconPapers)
JEL-codes: C02 G13 G22 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:64:y:2015:i:c:p:313-325

DOI: 10.1016/j.insmatheco.2015.06.006

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