Pricing life insurance contracts as financial options: the endowment policy case

In this paper, we consider the problem of pricing life insurance contracts using ideas and methods taken from option pricing theory. The methodology developed is, rather general, however, to fix the ideas, we focus our attention on the problem of pricing a pure endowment policy that has its life contingent payout linked to the performance of a risky asset. The behaviour of the value of the risky asset is modeled using a multiscale stochastic volatility model given by a system of three stochastic differential equations. The mortality risk is modeled via a stochastic differential equation that describes the time evolution of the mortality rate. Under the assumption that the financial and the mortality risks are independent, a formula to price the simplest pure endowment policy is derived. A computational method to evaluate the pricing formula derived is developed. Some numerical experiments on test problems are presented.