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.


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


[1] Abkemeier N., National Underwriter 103 (10) pp 7– (1999)
[2] Bingham N. H., Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives (1998) · Zbl 0922.90009
[3] Black F., Journal of Political Economy 81 pp 637– (1973) · Zbl 1092.91524
[4] Chance D. M., Journal of Financial Services Research 1 pp 335– (1988)
[5] Chen A. H., Journal of Financial Services Research 4 pp 93– (1990)
[6] Conze A., Journal of Finance 46 pp 1893– (1991)
[7] Cox J. C., Option Markets (1985)
[8] Gerber H. U., Transactions of the Society of Actuaries 46 pp 99– (1994)
[9] Gerber H. U., Insurance: Mathematics and Economics 18 pp 183– (1996) · Zbl 0896.62112
[10] Goldman M. B., Journal of Finance 34 pp 1111– (1979)
[11] Harrison J. M., Brownian Motion and Stochastic Flow Systems (1985) · Zbl 0659.60112
[12] Haug E. P., The Complete Guide to Option Pricing Formulas (1998)
[13] Horwitz E. J., National Underwriter 103 (2) pp 13– (1999)
[14] Hull J. C., Options, Futures, and Other Derivative Securities, 3. ed. (1997)
[15] Karr A. F., Probability (1993)
[16] King S. R., Federal Reserve Bank New York Quarterly Review 11 pp 9– (1987)
[17] Lo A. W., The Legacy of Nobert Wiener: A Centennial Symposium pp 49– (1997)
[18] Mitchell G. T., Society of Actuaries Study Note Number 441 pp 99– (1996)
[19] Panjer H. H., Financial Economics: With Applications to Investments, Insurance, and Pensions (1998)
[20] Shiryaev A. N., Essentials of Stochastic Finance: Facts, Models, Theory (1999)
[21] Tiong S., Actuarial Research Clearing House 1 pp 353– (2000)
[22] Wilmott P., Derivatives: The Theory and Practice of Financial Engineering (1998)
[23] Zhang P. G., Exotic Options: A Guide to Second Generation Options, 2. ed. (1998) · Zbl 0934.91030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.