Guaranteed annuity conversion options and their valuation∗

In this chapter, we consider a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain unit-linked pension contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract 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, in order to obtain a closed-form analytical solution to the fair valuation of the liabilities implied by these contracts. Mortality risk is incorporated via a stochastic model for the evolution over time of the underlying hazard rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key financial and mortality parameters is also analyzed.