Green nested simulation via likelihood ratio: Applications to longevity risk management

Abstract

In the context of longevity risk, the nested simulation problem arises in various applications such as evaluating the effectiveness of longevity hedges and estimating solvency capital requirements. The standard nested simulation method demands a lot of computational effort, thereby making risk analyses in these applications difficult, especially in a practical setting when computing power is constrained. In this paper, we propose a green nested simulation (GNS) procedure for longevity risk management. The GNS procedure requires only small computations, achieves high accuracies, and is easy to implement. Mathematically, the GNS estimator is unbiased, and, in different modes of convergence, can achieve an arbitrary accuracy as the simulation budget increases. We demonstrate the GNS procedure with three numerical case studies. The empirical results indicate that the GNS procedure leads to estimates that are orders of magnitudes more accurate compared to the standard nested simulation, and also outperforms the existing approximation methods for getting around the nested simulation problem, particularly when the payoff under consideration is non-linear.