Pricing of long dated equity-linked life insurance contracts

Abstract

This article adopts an approach to pricing of equity-linked life insurance contracts, which only requires the existence of the numéraire portfolio. An equity-linked life insurance contract is equivalent to a sum of the guaranteed amount and the value of an option on the equity index with some mortality risk attached. The numéraire portfolio equals the growth optimal portfolio and is used as numéraire or benchmark, where the real-world probability measure is taken as pricing measure. To obtain tractable solutions the short rate is modelled as a quadratic form of some Gaussian factor processes. Furthermore, the dynamics of the mortality rate is modelled as a threshold life table. The dynamics of the discounted equity market index or benchmark is modelled by a time transformed squared Bessel process. The equity-linked life insurance contracts are evaluated analytically.