Fair Value of Life Liabilities with Embedded Guarantees: an Application to a Portfolio of Italian Insurance Policies

In this paper we present a pricing application analyzing, in a contingent-claims framework, the two most common types of life policies sold in Italy during the last two decades. These policies, characterized by different premium payment styles (single and constant periodical), are endowments including both a bonus option and a surrender option. The bonus option’s benefit is annually adjusted according to the performance of a reference fund and a minimum return is guaranteed to the policyholder. The surrender option is an American-style put option that enables the policyholder to give up the contract receiving the surrender value. We propose to price this American-style put option by Montecarlo simulation according to the Longstaff and Schwartz Least-Squares approach giving a comparative analysis with the results obtained by Grosen and Jørgensen according to a Recursive Tree Binomial approach. We then proceed to present an application to a relevant portion of a major Italian life policies’ portfolio. We make use of a Black&Scholes-CIR economy to simulate the reference fund, composed by equities and bonds, according to De Felice and Moriconi and Pacati, and we estimate the fair value of portfolio’s liabilities extending the framework in order to price also the embedded surrender options.

Keywords: Surrender Option; Longstaff-Schwartz Least-Squares Approach; Minimum Interest Rate Guaranteed; Black&Scholes-CIR Framework.