Pricing and Hedging Guaranteed Annuity Options via Static Option Replication

In this paper we derive a market value for Guaranteed Annuity Optionusing martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanillainterest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical UK interest rate data from the period1980 until 2000 that the static replicating portfolio is extremely effective asa hedge against the interest rate risk involved in the GAO, that thestatic replicating portfolio is considerably cheaper than up-front reservingand also that the replicating portfolio provides a much better level ofprotection than an up-front reserve.