Valuation of guaranteed annuity conversion options.
The authors study unit-linked deferred annuity contracts purchased originally by a single premium. They introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in UK. The approach exploits the traditional option valuation procedure in order to provide indications in terms of pricing, reserving and hedging of the guaranteed annuity option contract. The option pricing approach that is proposed is based on similarity between the payoff structure of the contract under consideration and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath-Jarrow-Morton framework for the term structure of interest rates. Two alternative formulations of the HJM framework are given based on different specifications for the forward rate volatility. Under the additional assumption of an unsystematic mortality risk , independent of the financial risk, a general pricing framework is proposed and closed analytical formulae for the value of the guaranteed annuity options are obtained. Some numerical results and sensitivity analysis are presented.
scientific article; zbMATH DE number 2004036