Variable annuities: A unifying valuation approach |
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| Affiliation: | 1. Department of Business, Economics, Mathematics and Statistics ‘B. de Finetti’–University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy;2. Department of Economics–University of Parma, Via J.F. Kennedy 6, 43125 Parma, Italy;1. Department of Applied Mathematics, Kyung Hee University, Republic of Korea;2. Department of Mathematics, Hankuk University of Foreign Studies, Republic of Korea;1. Department of Mathematics and Statistics, Toronto, Ontario, Canada, M3J 1P3;2. CEPAR, Australia;3. School of Risk and Actuarial Studies, UNSW, Sydney, NSW 2052, Australia;1. Department of Mathematics, University of Connecticut, 196 Auditorium Rd U-3009, Storrs, CT, 06269, USA;2. Department of Statistical Sciences, University of Toronto, 100 St. George Street, Toronto, ON M5S 3G3, Canada;1. Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve Blvd. W., Montréal, Québec, Canada H3G 1M8;2. The Guardian Life Insurance Company of America, New York, NY, United States |
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| Abstract: | Life annuities and pension products usually involve a number of guarantees, such as minimum accumulation rates, minimum annual payments or a minimum total payout. Packaging different types of guarantees is the feature of so-called variable annuities. Basically, these products are unit-linked investment policies providing a post-retirement income. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in the case of death and survival. In this paper we propose a unifying framework for the valuation of variable annuities under quite general model assumptions. We compute and compare contract values and fair fee rates under ‘static’ and ‘mixed’ valuation approaches, via ordinary and least squares Monte Carlo methods, respectively. |
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