Longevity bond premiums: The extreme value approach and risk cubic pricing
AbstractThe purpose of this study is to analyze the securitization of longevity risk with an emphasis on longevity risk modeling and longevity bond premium pricing. Various longevity derivatives have been proposed, and the capital market has experienced one unsuccessful attempt by the European Investment Bank (EIB) in 2004. After carefully analyzing the pros and cons of previous securitizations, we present our proposed longevity bonds, whose payoffs are structured as a series of put option spreads. We utilize a random walk model with drift to fit small variations of mortality improvements and employ extreme value theory to model rare longevity events. Our method is a new approach in longevity risk securitization, which has the advantage of both capturing mortality improvements within sample and extrapolating rare, out-of- sample longevity events. We demonstrate that the risk cubic model developed for pricing catastrophe bonds can be applied to mortality and longevity bond pricing and use the model to calculate risk premiums for longevity bonds.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 46 (2010)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/inca/505554
IB13 IM01 IM10 IE10 Securitization Longevity risk Extreme value theory Bond spreads;
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- Alex Cowley & J. David Cummins, 2005. "Securitization of Life Insurance Assets and Liabilities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 193-226.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004.
"The basis risk of catastrophic-loss index securities,"
Journal of Financial Economics,
Elsevier, vol. 71(1), pages 77-111, January.
- J. David Cummins & David Lalonde & Richard D. Phillips, 2000. "The Basis Risk of Catastrophic-Loss Index Securities," Center for Financial Institutions Working Papers 00-22, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Kenneth A. Froot, 2001.
"The Market for Catastrophe Risk: A Clinical Examination,"
NBER Working Papers
8110, National Bureau of Economic Research, Inc.
- Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
- Kenneth A. Froot, 1999. "The Market for Catastrophe Risk: A Clinical Examination," NBER Working Papers 7286, National Bureau of Economic Research, Inc.
- Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751.
- Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Lin, Yijia & Cox, Samuel H., 2008. "Securitization of catastrophe mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 628-637, April.
- David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672.
- Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Angus Deaton & Christina Paxson, 2001.
"Mortality, Income, and Income Inequality Over Time in Britain and the United States,"
NBER Working Papers
8534, National Bureau of Economic Research, Inc.
- Angus S. Deaton & Christina Paxson, 2004. "Mortality, Income, and Income Inequality over Time in Britain and the United States," NBER Chapters, in: Perspectives on the Economics of Aging, pages 247-286 National Bureau of Economic Research, Inc.
- Angus Deaton & Christina Paxson, 2001. "Mortality, Income, And Income Inequality Over Time In Britain And The United States," Working Papers 267, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Health and Wellbeing..
- Michel Denuit & Pierre Devolder & Anne-Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113.
- J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk-Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545.
- Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Blake, David & Courbage, Christophe & MacMinn, Richard & Sherris, Michael, 2011.
"Longevity risks and capital markets: The 2010-2011 update,"
34279, University Library of Munich, Germany.
- David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(4), pages 489-500, October.
- Biffis, Enrico & Blake, David & Pitotti, Lorenzo & Sun, Ariel, 2011. "The cost of counterparty risk and collateralization in longevity swaps," MPRA Paper 35740, University Library of Munich, Germany.
- Blake, David & Brockett, Patrick & Cox, Samuel & MacMinn, Richard, 2011. "Longevity risk and capital markets: The 2009-2010 update," MPRA Paper 28868, University Library of Munich, Germany.
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