The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case

In this paper, we extend the analysis of the behaviour of pension contracts with guaranteed annuity conversion options (as presented in Ballotta and Haberman [Insurance: Math. Econ. 33 (2003) 87]) to the case in which mortality risk is incorporated via a stochastic model for the evolution over time of the underlying hazard rates. The pricing framework makes also use of a Black–Scholes/Heath–Jarrow–Morton economy in order to obtain an analytical solution to the fair valuation problem of the liabilities implied by these particular pension policies. The solution is not in closed form, and therefore, we resort to Monte Carlo simulation. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters from the financial and mortality models is also analyzed.