On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

In recent years, market consistent-valuation approaches have gained an increasing importance for the insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.

In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.

Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and generalized Black-Scholes set-up, respectively. Moreover, we study the impact of the considered early exericse feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Levy model.

Keywords: Life insurance; Risk-neutral valuation; Embedded options; Bermudan options; Nested simulations; PDE methods; Least-squares Monte Carlo.