Risk-neutral valuation of participating life insurance contracts. (English) Zbl 1098.91067

Summary: The valuation of life insurance contracts using concepts from financial mathematics has recently attracted considerable interest in academia as well as among practitioners. In this paper, we will investigate the valuation of participating contracts, which are characterized by embedded interest rate guarantees and some bonus distribution rules. We will model these under the specific regulatory framework in Germany; however, our analysis can be applied to any insurance market with cliquet-style guarantees. We will present a framework, in which different kinds of guarantees or options can be analyzed separately. Also, the practical implementation of such models is discussed. We use two different numerical approaches to derive fair parameter settings of such contracts and price the embedded options.The sensitivity of the contract value with respect to multiple parameters is studied. In particular, we find that life insurers offer interest rate guarantees below their risk-neutral value. Furthermore, the financial strength of an insurance company considerably affects the value of a contract.


91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI


[1] Aase, K.; Persson, S., Pricing of unit-linked life insurance policies, Scandinavian actuarial journal, 1, 26-52, (1994) · Zbl 0814.62067
[2] Bacinello, A.R., Fair pricing of life insurance partcipating policies with a minimum interest rate guaranteed, Astin bulletin, 31, 275-297, (2001) · Zbl 1098.91537
[3] Bacinello, A.R., Fair valuation of a guaranteed life insurance participating contract embedding a surrender option, The journal of risk and insurance, 70, 461-487, (2003)
[4] Bauer, D., 2005. Modellierung und Risikoneutrale Bewertung eines Deutschen Lebensversicherungsvertrages. Diploma Thesis, University of Ulm
[5] Brennan, M.J.; Schwartz, E.S., The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of financial economics, 3, 195-213, (1976)
[6] Grosen, A.; Jensen, B.; Jørgensen, P.L., A finite difference approach to the valuation of path dependent life insurance liabilities, Geneva papers on risk and insurance theory, 26, 57-84, (2001)
[7] Grosen, A.; Jørgensen, P.L., Fair valuation of life insurance liablities: the impact of interest guarantees, surrender options, and bonus policies, Insurance: mathematics and economics, 26, 37-57, (2000) · Zbl 0977.62108
[8] Hansen, M.; Miltersen, K.R., Minimum rate of return guarantees: the danish case, Scandinavian actuarial journal, 4, 280-318, (2002) · Zbl 1039.91040
[9] Kling, A., Richter, A., Ruß, J., 2004. The interaction of guarantees, surplus distribution, and asset allocation in with profit life insurance policies. Working Paper, University of Ulm and Illinois State University · Zbl 1273.91238
[10] Miltersen, K.R.; Persson, S.A., Guaranteed investment contracts: distributed and undistributed excess return, Scandinavian actuarial journal, 4, 257-279, (2003) · Zbl 1092.91053
[11] Tanskanen, A.J.; Lukkarinen, J., Fair valuation of path-dependent participating life insurance contracts, Insurance: mathematics and economics, 33, 595-609, (2004) · Zbl 1103.91373
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.