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

Daniela Bergmann · Rüdiger Kiesel

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Stochastic processes and financial applications Insurance and Financial Risk Management Probability and Risk Models

Abstract

Abstract In recent years, market-consistent valuation approaches have gained an increasing importance for 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 a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.

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References

1977An equilibrium characterization of the term structure 2003Options, Futures and Other Derivatives 2003Monte Carlo Methods in Financial Engineering 2001Valuing American Options by Simulation: A Simple Least-Squares Approach 2003Financial Modelling with Jump Processes 2008A General Version of the Fundamental Theorem of Asset Pricing (1994)1994A general version of the fundamental theorem of asset pricing 1997Processes of normal inverse Gaussian type

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