Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach
Variable annuities (VAs) represent a marked change from earlier life products in the guarantees that they offer and it is no longer possible to manage the risks of these liabilities using traditional actuarial methods. Thinking about guarantees as options suggests applying risk neutral pricing in order to value the embedded guarantees, such as guaranteed minimum death benefits (GMDBs). However, due to the long maturities of contracts, stochastic volatility and many other reasons, VA markets are incomplete. In this paper we propose a methodology for pricing GMDBs under a benchmark approach which does not require the existence of a risk neutral probability measure. We assume that the insurance company invests in the growth optimal portfolio of its investment universe and apply real world pricing rather than risk neutral pricing. In particular, we consider the minimal market model and conclude that in this setup the fair price of a roll-up GMDB is lower than the price obtained by applying standard risk neutral pricing. Moreover, we take into account rational as well as irrational lapsation of the policyholder.
|Date of creation:||01 Apr 2008|
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- David Heath & Eckhard Platen, 2002.
"Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model,"
Research Paper Series
78, Quantitative Finance Research Centre, University of Technology, Sydney.
- David Heath & Eckhard Platen, 2002. "Consistent pricing and hedging for a modified constant elasticity of variance model," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 459-467.
- Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
- Bühlmann, Hans & Platen, Eckhard, 2003. "A Discrete Time Benchmark Approach for Insurance and Finance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(02), pages 153-172, November.
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