Calibrating affine stochastic mortality models using term assurance premiums

Abstract

In this paper, we focus on the calibration of affine stochastic mortality models using term assurance premiums. We view term assurance contracts as a “swap” in which policyholders exchange cash flows (premiums vs. benefits) with an insurer analogous to a generic interest rate swap or credit default swap. Using a simple bootstrapping procedure, we derive the term structure of mortality rates from a stream of contract quotes with different maturities. This term structure is used to calibrate the parameters of affine stochastic mortality models where the survival probability is expressed in closed form. The Vasicek, Cox–Ingersoll–Ross, and jump-extended Vasicek models are considered for fitting the survival probabilities term structure. An evaluation of the performance of these models is provided with respect to premiums of three Italian insurance companies.