Valuation perspectives and decompositions for variable annuities with GMWB riders |
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| Affiliation: | 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;1. Head of Unit-Group Risk Management at Generali, Milan, Italy;2. Department of Management, Economics and Quantitative Methods, University of Bergamo, Bergamo, Italy;3. EDHEC Business School in Nice, France;1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, China;2. School of Risk and Actuarial Studies and CEPAR, UNSW Business School, The University of New South Wales, Sydney, NSW 2052, Australia;3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;1. Department of Information and Financial Management and Institute of Finance, National Chiao-Tung University, Taiwan;2. Department of Finance, National Central University, Taiwan;3. Risk and Insurance Research Center, College of Commerce, National Chengchi University, Taiwan;1. School of Business, Stevens Institute of Technology, Babbio Center, 1 Castle Point on Hudson, Hoboken, NJ 07310, USA;2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30318, USA;3. Department of Mathematics, Marist College, 3399 North Road, Poughkeepsie, NY 12601, USA;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 |
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| Abstract: | The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of periodic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider from a financial economic perspective. Particular focus is placed on the distinct perspectives of the insurer and policyholder and the unifying relationship. We extend a decomposition of the VA contract into components that reflect term-certain payments and embedded derivatives to the case where the policyholder has the option to surrender, or lapse, the contract early. |
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| Keywords: | Variable annuity GMWB Optimal stopping |
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