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

Published online by Cambridge University Press:  09 August 2013

Daniel Bauer ,
Daniela Bergmann  and
Rüdiger Kiesel
Daniela Bergmann
Affiliation:
Institute of Insurance, Ulm University, Helmholtzstraβe 18, 89069 Ulm, Germany, Tel.: +49-731-50-31187, Fax: +49-731-50-31239, [email protected]
Rüdiger Kiesel
Affiliation:
Chair for Energy Trading and Financial Services, University of Duisburg-Essen, and, Centre of Mathematics for Applications, University of Oslo, Universitätsstraβe 12, 45141 Essen, Germany, Tel.: +49-201-183-4963, Fax: +49-201-183-4974, [email protected]
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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.

Keywords

Life insuranceRisk-neutral valuationEmbedded optionsBermudan optionsNested simulationsPDE methodsLeast-squares Monte Carlo
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 65 - 95
Copyright
Copyright © International Actuarial Association 2010

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