Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results

We propose a pricing model for life insurance policies in which the benefits are linked to the performance of a portfolio of interest rate sensitive assets (reference fund), and a minimum guarantee provision is present. The model is cast in the celebrated term structure framework developed by Cox, Ingersoll and Ross. As for the behaviour of the investment component, we analyse two polar cases. In the first one the payments due on the reference fund when the contract is still ‘alive’ are not reinvested, while in the second case we propose a reinvestment policy. We show how to obtain a closed form solution for the single premium in the no-reinvestment case, and how to implement a simulation approach to calculate numerically the single premium in the reinvestment case. We illustrate our analysis with numerical results that help in understanding the comparative static properties of the models proposed.