In this paper we derive a market value for with-profits guaranteed annuity options (GAOs) using martingale modelling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the with-profits GAO. Finally, we illustrate with historical UK interest rate data from the period 1980 to 2000 that the static replicating portfolio would have been extremely effective as a hedge against the interest rate risk involved in the GAO, that the static replicating portfolio would have been considerably cheaper than up-front reserving and also that the replicating portfolio would have provided a much better level of protection than an up-front reserve.

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Insurance: Mathematics and Economics
Erasmus Research Institute of Management

Pelsser, A.A.J. (2003). Pricing and hedging guaranteed annuity options via static option replication. Insurance: Mathematics and Economics, 33(2), 283–296. doi:10.1016/S0167-6687(03)00154-9