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Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds*

  • Alexandros A. Zimbidis (a1), Nickolaos E. Frangos (a1) and Athanasios A. Pantelous (a1)

Abstract

The aim of the paper is twofold. Firstly, to analyze the historical data of the earthquakes in the boarder area of Greece and then to produce a reliable model for the risk dynamics of the magnitude of the earthquakes, using advanced techniques from the Extreme Value Theory. Secondly, to discuss briefly the relevant theory of incomplete markets and price earthquake catastrophe bonds, combining the model found for the earthquake risk and an appropriate model for the interest rate dynamics in an incomplete market framework. The paper ends by providing some numerical results using Monte Carlo simulation techniques and stochastic iterative equations.

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Copyright

Footnotes

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This work was supported by the reinforcement program of Human Research Manpower #8211 “PENED” in the framework of Measure 8.3, Action 8.3.1 of the Operational program of competitiveness #8211; Third Community Support Program.

Footnotes

References

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Bank of Greece (2005) Financial Bulletin (in Greek) 25, August 2005.
Banks, J., Carson, S.J. II, Nelson, L.B. and Nicol, M.D. (2001) Discrete-Event System Simulation. Prentice Hall International Series in Industrial and System Engineering, U.S.A.
Baryshnikov, Y., Mayo, A. and Taylor, D.R. (2001) Pricing of CAT Bonds.
Baxter, M. and Rennie, A. (1999) Financial Calculus: An introduction to derivative pricing. Cambridge University Press, U.K.
Beelders, O. and Colarossi, D. (2004) Modeling Mortality Risk with Extreme Value Theory: The Case of Swiss Re’s Mortality-Indexed Bonds. Global Association of Risk Professionals 19, 2630.
Beirlant, J., Teugels, J. and Vynckier, P. (1996) Practical Analysis of Extreme Value. Leuven University Press, Belgium.
Boyle, P., Broadie, M. and Glasserman, (1997) Monte Carlo methods and security pricing. Journal of Economics 21, 89
Bratley, P., Fox, L.B. and Schrage, E.L. (1987) A Guide to Simulation. Springer, 2nd Edition, U.S.A.
Briys, E. (1997) From Genoa to Kobe: Natural Hazards, Insurance Risks and the Pricing of Insurance-Linked Bonds. Lehman Brothers International, London U.K.
Coles, S. (2004) An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics, 3rd edition, Great Britain.
Coles, S. (2004) “S-plus Functions for Extreme Value Modeling”. http://www.maths.bris.ac.uk/~masgc/ismev/summary.html.
Cox, H.S. and Pedersen, W.H. (2000) Catastrophe Risk Bonds. N.A.A.J. 4(4), 5682.
Cummins, D. and Geman, H. (1995) Pricing Catastrophe Futures and Call Spreads: An Arbitrage Approach. Journal of Fixed Income 4, 4657.
D’Archy, S.P. and France, G.V. (1992) Catastrophe Futures: A Better Hedge for Insurers. Journal of Risk and Insurance 59, 575600.
Embrechts, P., Klüppelberg, C. and Mikosch, T. (2003) Modelling Extremal Events. Springer, 4th edition, Germany.
Embrechts, P., Resnick, I.S. and Samorodnitsky, G. (1999) Extreme Value Theory as a Risk Management Tool. N.A.A.J. 3(2), 3041.
EURIBOR Historical Data (EURIBOR organization): http://www.euribor.org
Fisher, R.A. and Tippett, L.H.C. (1928) On the estimation of the frequency distributions of the largest or smallest number of a sample. Proceedings of the Cambridge Philosophical Society 24, 180190.
Gnedenko, B.V. (1943) Sur la distribution limite du terme maximum d’une série alétoire. Annals of Mathematics 44, 423453.
Hosking, J.R.M. (1986) Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. Applied Statistics 34, 301310.
Institute of Geodynamics, National Observatory of Athens (IG-NOA). At World Wide Web address: http://www.gein.noa.gr/services/cat.html
Jenkinson, A.F. (1969) Statistic of Extremes. Technical Note 98, World Meteorological Organization. Chapter 5, 183227.
Kellison, G.S. (1991) The Theory of Interest. Irwin/McGraw-Hill. U.S.A.
Kotz, S. and Nadarajah, (2002) Extreme Value Distributions: Theory and Applications. Imperial College Press, Singapore.
Lee, J.-P. and Yu, M.-T. (2002) Pricing Default-Risky CAT Bonds with Moral Hazard and Basis Risk. The Journal of Risk and Insurance 69(1), 2544.
Loubergé, H., Kellezi, E. and Gilli, M. (1999) Using Catastrophe-Linked Securities to Diversify Insurance Risk: A Financial Analysis of Cat Bonds. Journal of Insurance Issues 22, 125146.
Macleod, A.J. (1989) Comment on Maximum-Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Applied Statistics 38, 198199.
McNeil, J.A. (1997) Estimating the tails of Loss Severity distributions using Extreme Value Theory. ASTIN Bulletin 27(1), 117137.
McNeil, J.A. (2001) “EVIS, version 4”. http://www.math.ethz.ch/~mcneil/software.html
Miller, G. (Senior Vice President and Deputy General Counsel of the Bond Market Association) and De Konkoly, Th.M. (Vice President and Associate General Counsel of the Bond Market Association) (2002) Comments on Draft GAO report “Catastrophe Insurance Risks: The Role of Risk-Linked Securities and Factors Affecting their Use”. GAO-02-941
Nutter, W.F. (President of Reinsurance Association of America (RAA)) (2002) Comments on the GAO’s preliminary report entitled “Catastrophe Insurance Risks”. GAO-02-941.
O’Brien, T. (1997) Hedging Strategies Using Catastrophe Insurance Options. Insurance: Mathematics and Economics 21, 153162.
Øksendal, B. (2003) Stochastic Differential Equations. Springer, 6th edition, Germany.
Papanastassiou, D., Latoussakis, J. and Stavrakakis, G. (2001) “Proceedings of the 9th International Congress of the Geological Society of Greece”, Athens, September 2001. Bulletin of the Geological Society of Greece XXXIV/4, 15631566.
Prescott, P. and Walden, A.T. (1980) Maximum Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Biometrika 67, 723724.
Prescott, P. and Walden, A.T. (1983) Maximum Likelihood Estimation of the Parameters of the Three-Parameter Generalized Extreme-Value Distribution from Censored Samples. J. Statist. Comput. Simulation 16, 241250.
Resnick, I.S. (1997) Discussion of the Danish Data on Large Fire Insurance Losses. ASTIN Bulletin 27(1), 139151.
Romaniuk, M. (2002) Pricing the risk-transfer financial instruments via Monte Carlo methods. Interium Report IR-02-065 for International Institute for Applied Systems Analysis (Approved by Ermoliev Yuri).
Romaniuk, M. (2003) Pricing the risk-transfer financial instruments via Monte Carlo methods. System Analysis Modelling Simulation 43(8), 10431064.
United States General Accounting Office (2002) Catastrophe Insurance Risks: The Role of Risk-Linked Securities and Factors Affecting their Use. GAO-02-941.
United States General Accounting Office (2005) Catastrophe Risk: U.S. and European Approaches to Insure Natural Catastrophe and Terrorism Risks. GAO-05-199.
United States General Accounting Office (2006) Federal Emergency Management Agency: Challenges for the National Flood Insurance Program. GAO-06-335T.
Vaugirard, V. (2003) Pricing Catastrophe Bonds by an Arbitrage Approach. The Quarterly Review of Economics and Finance 43, 119132.
Vaugirard, V. (2004) A Canonical First Passage Time Model to Pricing Nature-Linked Bonds. Economic Bulletin 7(2), 17.
Young, R.V. (2004) Pricing an Incomplete Market with in an Affine Term Structure. Mathematical Finance 14(3), 359381.

Keywords

Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds*

  • Alexandros A. Zimbidis (a1), Nickolaos E. Frangos (a1) and Athanasios A. Pantelous (a1)

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