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Pricing and Hedging Guaranteed Annuity Options via Static Option Replication

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Author Info
Antoon Pelsser () (Faculty of Economics, Erasmus University Rotterdam)

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Abstract

In this paper we derive a market value for Guaranteed Annuity Option using martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical UK interest rate data from the period 1980 until 2000 that the static replicating portfolio is extremely effective as a hedge against the interest rate risk involved in the GAO, that the static replicating portfolio is considerably cheaper than up-front reserving and also that the replicating portfolio provides a much better level of protection than an up-front reserve.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-037/2.

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Date of creation: 10 Apr 2002
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Handle: RePEc:dgr:uvatin:20020037

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June. [Downloadable!] (restricted)
  2. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November. [Downloadable!] (restricted)
  3. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179. [Downloadable!] (restricted)
  4. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  5. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06. [Downloadable!] (restricted)
  6. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330. [Downloadable!] (restricted)
  7. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March. [Downloadable!] (restricted)
  8. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March. [Downloadable!] (restricted)
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  9. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February. [Downloadable!] (restricted)
  10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  11. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Thomas Post, 2009. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality," SFB 649 Discussion Papers SFB649DP2009-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Quantitative Finance Papers 0908.3196, arXiv.org. [Downloadable!]
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