Pricing and Hedging Guaranteed Annuity Options via Static Option Replication

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.