Annuity contract valuation under dependent risks

Abstract

A pricing framework for annuity valuation is considered, where the dependence between interest and mortality risk factors is modelled explicitly. The calculation is facilitated by combining the change of measure and comonotonic-based methods to obtain accurate approximation of the survival probability’s quantile and hence annuity value. We demonstrate that our approach is significantly more efficient than simulation under a stochastic setting. The interest rate is governed by a two-factor Hull–White model to capture current levels of very low and even the possibility of negative rates occurring in some countries post-2008 financial crisis. The mortality rate evolves in accordance with a continuous-time version of the Lee–Carter model.