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Valuing equity-indexed annuities. With discussion by G. Thomas Mitchell and Hans U. Gerber and Elias S. W. Shiu. (English) Zbl 1083.62545

Summary: Equity-indexed annuities have generated a great deal of interest and excitement among both insurers and their customers since they were first introduced to the marketplace in early 1995. Because of the embedded options in these products, the insurers are presented with some challenging mathematical problems when it comes to the pricing and management of equityindexed annuities. This paper explores the pricing aspect of three of the most common product designs: the point-to-point, the cliquet, and the lookback. Based on certain assumptions, we are able to present the pricing formulas in closed form for the three product designs. The method of Esscher transforms is the fundamental tool for pricing such deferred annuities.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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