Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-23T18:05:52.969Z Has data issue: false hasContentIssue false
  • English
  • Français

HEDGING MORTALITY CLAIMS WITH LONGEVITY BONDS*

Published online by Cambridge University Press:  18 June 2013

Francesca Biagini ,
Thorsten Rheinländer  and
Jan Widenmann
Francesca Biagini
Affiliation:
Department of Mathematics, LMU Munich, Theresienstr. 39, 80333 Munich, Germany E-Mail: francesca.biagini@math.lmu.de
Thorsten Rheinländer*
Affiliation:
Research Group Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/E105, A-1040 Vienna, Austria
Jan Widenmann
Affiliation:
Department of Mathematics, LMU Munich, Theresienstr. 39, 80333 Munich, Germany E-Mail: jan.widenmann@math.lmu.de
*
E-Mail: rheinlan@fam.tuwien.ac.at
Get access Rights & Permissions [Opens in a new window]

Abstract

We study mean–variance hedging of a pure endowment, a term insurance and general annuities by trading in a longevity bond with continuous rate payments proportional to the survival probability. In particular, we discuss the introduction of a gratification annuity as an interesting insurance product for the life insurance market. The optimal hedging strategies are determined via their Galtchouk–Kunita–Watanabe decompositions under specific, yet sufficiently general model assumptions. The results are then further illustrated by assuming a general affine structure of the mortality intensity process. The optimal hedging strategies as well as the residual hedging error of a gratification annuity and a simple life annuity are finally investigated with numerical simulations, which illustrate the nice features of the gratification annuity for the insurance industry.

Keywords

Mean-variance hedginglife insurancelongevity bondintensity-based approachaffine mortality intensity
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 123 - 157
Copyright
Copyright © ASTIN Bulletin 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. (228087).

References

[1]Barbarin, J. (2008a) Heath–Jarrow–Morton modelling of longevity bonds and the risk minimization of life insurance portfolios. Insurance: Mathematics and Economics, 43 (1), 41–55.Google Scholar
[2]Barbarin, J. (2008b) Valuation, Hedging and the Risk Management of Insurance Contracts. PhD thesis, Université Catholique de Louvain.Google Scholar
[3]Barrieu, P. and Albertini, L. (eds.) (2009) The Handbook of Insurance-Linked Securities. Chichester: Wiley.Google Scholar
[4]Biagini, F. and Cretarola, A. (2012) Local risk-minimization for defaultable claims with recovery process. Applied Mathematics & Optimization, 65, 293–314.CrossRefGoogle Scholar
[5]Biagini, F. and Schreiber, I. (2012) Risk minimization for life insurance liabilities. Working Paper, University of Munich.Google Scholar
[6]Bielecki, T.R. and Rutkowski, M. (2004) Credit Risk: Modelling, Valuation and Hedging, 2nd ed. Berlin: Springer-Finance.CrossRefGoogle Scholar
[7]Biffis, E. (2005) Affine processes for dynamic mortality and actuarial valuation. Insurance: Mathematics and Economics, 37 (3), 443–468.Google Scholar
[8]Biffis, E. and Millossovich, P. (2006) A bidimensional approach to mortality risk. Decisions in Economics and Finance, 29 (2), 71–94.CrossRefGoogle Scholar
[9]Blake, D., Boardman, T. and Cairns, A.J.G. (2010) Longevity risk: Why governments should issue longevity bonds. Discussion Paper. Pensions Institute.CrossRefGoogle Scholar
[10]Blake, D. and Burrows, W. (2001) Survivor bonds: Helping to hedge mortality risk. Journal of Risk and Insurance, 68 (2), 336–348.CrossRefGoogle Scholar
[11]Blake, D., Cairns, A.J.G. and Dowd, K. (2006) Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin, 36 (1), 79–120.Google Scholar
[12]Blake, D., Cairns, A.J.G. and Dowd, K. (2008) The birth of the life market. Asia-Pacific Journal of Risk and Insurance, 3 (1), 6–36.CrossRefGoogle Scholar
[13]Blanchet-Scalliet, C. and Jeanblanc, M. (2004) Hazard rate for credit risk and hedging defaultable contingent claims. Finance & Stochastics, 8 (1), 145–159.CrossRefGoogle Scholar
[14]Coculescu, D., Jeanblanc, M. and Nikeghbali, A. (2008) Default times, non arbitrage conditions and change of probability measures. Working Paper, University of Zurich, Université d'Evry.Google Scholar
[15]Dahl, M., Melchior, M. and Møller, T. (2008) On systematic mortality risk and risk-minimization with survivor swaps. Scandinavian Actuarial Journal, 2 (2), 114–146.CrossRefGoogle Scholar
[16]Dahl, M. and Møller, T. (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Mathematics and Economics, 39 (2), 193–217.CrossRefGoogle Scholar
[17]Duffie, D., Filipović, D. and Schachermayer, W. (2003) Affine processes and applications in finance. Annals of Applied Probability, 13 (3), 984–1053.CrossRefGoogle Scholar
[18]Luciano, E. and Vigna, E. (2008) Mortality risk via affine stochastic intensities: Calibration and empirical relevance. Belgian Actuarial Bulletin, 8, 5–16.Google Scholar
[19]Møller, T. (1998) Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28 (1), 17–47.CrossRefGoogle Scholar
[20]Møller, T. (2001) Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics, 5 (4), 419–446.Google Scholar
[21]Norberg, R. (2006) The pension crisis: Its causes, possible remedies, and the role of the regulator. Erfaringer og utfordringer, 20 years Jubilee Volume of Kredittilsynet, the Financial Supervisory Authority of Norway.Google Scholar
[22]Norberg, R. (2013) Optimal hedging of demographic risk in life insurance. Finance and Stochastics, 17 (1), 197–222.CrossRefGoogle Scholar
[23]Protter, P.E. (2005) Stochastic Integration and Differential Equations, 2nd ed. New York: Springer.CrossRefGoogle Scholar
[24]Schrager, D.F. (2006) Affine stochastic mortality. Insurance: Mathematics and Economics, 38 (1), 81–97.Google Scholar
[25]Schweizer, M. (2001) A guided tour through quadratic hedging approaches. In Option Pricing, Interest Rates and Risk Management, (ed. Jouini, E., Cvitanic, J. and Musiela, M.), pp. 538–574. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
[26]Wadsworth, M., Findlater, A. and Boardman, T. (2001) Reinventing annuities. Working Paper, Staple Inn Society.Google Scholar