A generalized pricing framework addressing correlated mortality and interest risks: a change of probability measure approach

Annuity-contingent derivatives involve both mortality and interest risks, which could have a correlation. In this article, we propose a generalized pricing framework in which the dependence between the two risks can be explicitly modelled. We also utilize the change of measure technique to simplify the valuation expressions. We illustrate our methodology in the valuation of a guaranteed annuity option (GAO). Using both forward measure associated with the bond price as numéraire and the newly introduced concept of endowment-risk-adjusted measure, we derive a simplified formula for the GAO price under the generalized framework. Numerical results show that the methodology proposed in this article is highly efficient and accurate.