Pricing of multi-period rate of return guarantees

The basis for this paper is the pricing of multi-period rate of return guarantees. These guarantees can typically be found in life insurance and pension contracts. We derive closed form solutions, expressed by the cumulative multivariate normal probability distribution, for multi-period rate of return guarantees on both a money market account and a stock. The guarantees of Hipp (1996), Persson and Aase (1997), and Miltersen and Persson (1999) [Options for guaranteed index-linked life insurance, in: Proceedings of the AFIR 1996, 1996, pp. 1463–1483; J. Risk Insur. 64 (4) (1997) 599; Insur.: Math. Econ. 25 (3) (1999) 307] are special cases of our results.