  In this paper, we are concerned with the valuation of Guaranteed Annuity
Options (GAOs) under the most generalised modelling framework where both
interest and mortality rates are stochastic and correlated. Pricing these type
of options in the correlated environment is a challenging task and no closed
form solution exists in the literature. We employ the use of doubly stochastic
stopping times to incorporate the randomness about the time of death and employ
a suitable change of measure to facilitate the valuation of survival benefit,
there by adapting the payoff of the GAO in terms of the payoff of a basket call
option. We derive general price bounds for GAOs by utilizing a conditioning
approach for the lower bound and arithmetic-geometric mean inequality for the
upper bound. The theory is then applied to affine models to present some very
interesting formulae for the bounds under the affine set up. Numerical examples
are furnished and benchmarked against Monte Carlo simulations to estimate the
price of a GAO for a variety of affine processes governing the evolution of
mortality and the interest rate.
