The Life Care Annuity: enhancing product features and refining pricing methods

In this paper we provide more general features for the variable annuity contract with LTC payouts and GLWB proposed by the state-of-the-art and we refine its pricing methods. In particular, as to product features, we allow dynamic withdrawal strategies, including the surrender option. Furthermore, we consider stochastic interest rate, described by a Cox-Ingersoll-Ross (CIR) process. As to the numerical methods, we solve the stochastic control problem involved by the selection of the optimal withdrawal strategy by means of a robust tree method. We use such a method to estimate the fair price of the product. Furthermore, our numerical results show how the optimal withdrawal strategy varies over time with the health status of the policyholder. Our proposed tree method, we name Tree-LTC, proves to be efficient and reliable, when tested against the Monte Carlo approach.