Fair valuation of participating policies in a stochastic interest rate framework

Participating policies are innovative life insurance products that combine financial and demographic risks, and provide benefits linked to the company asset returns. Interest is credited periodically to the policy according to some bonus distribution rules. Such policies are generally equipped with a minimum interest rate guarantee and with a surrender option, which allows the holder to sell the policy back to the insurance company before its maturity versus the payment of a cash surrender value. Hence, numerical methods are required to evaluate participating policies due to the unknown distribution of the optimal surrender time. Under a constant interest rate framework, participating policies with a minimum interest guarantee have been evaluated by Bacinello [2], Chu and Kwok [4], and Bauer et al. [3], while Grosen and Jorgensen [5] and Bacinello [1] propose evaluation models for participating policies embedding both a minimum guaranteed bonus rate and a surrender option. Such insurance instruments are generally long-term contracts for which it is more appropri- ate to consider a stochastic dynamics for the interest rate than keeping it fixed for the entire policy lifetime. Our proposal moves in this direction in that it is suitable for evaluating participating policies embedding not only a minimum guaranteed bonus rate but also a surrender option in a stochastic interest rate framework. The model is flexible in that it may accommodate the different specifications for the stochastic interest rate widely used in finance, which are directly discretized by means of a recombining lattice approximation. Taking into account the stochastic rate, a similar lattice method is used to discretize the company asset dynamics. Then, the two lattices are combined in order to establish a bivariate tree where participating policy may be evaluated by discounting the policy payoff over the lattice branches, and allowing early exercise at each contract anniversary to model the surrender decision.