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-futurelifetimes 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.
approximated by a linear combination of geometric distributions, it suffices to consider curtate-futurelifetimes 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.
| Original language | English |
|---|---|
| Pages (from-to) | 313-325 |
| Number of pages | 13 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 64 |
| DOIs | |
| Publication status | Published - 15 Sept 2015 |
| Externally published | Yes |
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Gerber, H., Siu, E., & Yang, H. (2015). Geometric stopping of a random walk and its applications to valuing equity-linked death benefits. Insurance: Mathematics and Economics, 64, 313-325. https://doi.org/10.1016/j.insmatheco.2015.06.006