Fair Valuation of the Surrender Option Embedded in a Guaranteed Life Insurance Participating Policy

In this paper we deal with the problem of valuing the surrender option embedded in a participating life insurance policy with a minimum interest rate guaranteed. This feature is an American-style put option that enables the policyholder to sell back the contract to the insurer at the surrender value. By means of a recursive binomial tree à la Cox, Ross and Rubinstein (1979) we compute, first of all, the total price of the contract, which includes also a “bonus” option. Then this price is split into the value of three components: the basic contract, the bonus option and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.