Computing Risk Measures of Life Insurance Policies through the Cox–Ross–Rubinstein Model

Abstract

The problem of computing risk measures of life insurance policies is complicated by the fact that two different probability measures, the real-world probability measure along the risk horizon and the risk-neutral one along the remaining time interval, have to be used. This implies that a straightforward application of the Monte Carlo method is not available and the need arises to resort to time consuming nested simulations or to the least squares Monte Carlo approach. We propose to compute common risk measures by using the celebrated binomial model of Cox, Ross, and Rubinstein (1979) (CRR). The main advantage of this approach is that the usual construction of the CRR model is not influenced by the change of measure and a unique lattice can be used along the whole policy duration. Numerical results highlight that the proposed algorithm computes highly accurate values.