The Role of the Dependence between Mortality and Interest Rates When Pricing Guaranteed Annuity Options

Abstract

In this paper we investigate the consequences on the pricing of insurance contingent claims when we relax the typical independence assumption made in the actuarial literature between mortality risk and interest rate risk. Starting from the Gaussian approach of Liu et al. (2014), we consider more general affine models where the mortality and interest rates remain positive and we derive pricing formulas for insurance contracts like Guaranteed Annuity Options (GAOs). In a Wishart affine model, which allows for a non-trivial dependence between the mortality and the interest rates, we go far beyond the results found in the Gaussian case by Liu et al. (2014), where the value of these insurance contracts can be explained only in terms of the initial pairwise linear correlation.

Keywords: Wishart process, Guaranteed Annuity Options, Stochastic mortality, Stochastic interest rates, Affine interest rate models, Dependence, Fourier

JEL Classification: C00