A lattice approach to evaluate participating policies in a stochastic interest rate framework

To achieve the accurate evaluation and management of the risk affecting long-term life insurance contracts, the insurer cannot leave aside the consideration of stochastic dynamics not only for the company's assets but also for the interest rate. The aim of this paper is to provide, in such a framework, a flexible method for evaluating participating policies, life insurance products that combine financial and demographic risks, and provide benefits linked to the company's asset returns. Participating policies embedding not only a minimum guaranteed bonus rate but also a surrender option are analyzed. The method is flexible in that it allows the insurer to choose the most appropriate dynamics, both for the interest rate and the company's asset, among the ones widely diffused in finance. Lattice-based procedures are used to discretize the continuous time processes, and to provide a comprehensive evaluation method.