Valuation of Guaranteed Annuity Options in Affine Term Structure Models

Abstract

We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include stochastic duration approach, Edgeworth expansion and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.