Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-25T05:06:15.964Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  17 April 2015

Alexandros A. Zimbidis ,
Nickolaos E. Frangos  and
Athanasios A. Pantelous
Alexandros A. Zimbidis
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patision 76, 104 34 Athens, Greece, E-mails: aaz@aueb.gr, nef@aueb.gr, apantel@aueb.gr
Nickolaos E. Frangos
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patision 76, 104 34 Athens, Greece, E-mails: aaz@aueb.gr, nef@aueb.gr, apantel@aueb.gr
Athanasios A. Pantelous
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patision 76, 104 34 Athens, Greece, E-mails: aaz@aueb.gr, nef@aueb.gr, apantel@aueb.gr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

Extreme Value TheoryCatastrophe BondsMonte Carlo SimulationIterative Stochastic EquationsIncomplete Market
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 1 , May 2007 , pp. 163 - 183
Copyright
Copyright © ASTIN Bulletin 2007

Footnotes

*

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.

References

Bank of Greece (2005) Financial Bulletin (in Greek) 25, August 2005.Google Scholar
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.Google Scholar
Baryshnikov, Y., Mayo, A. and Taylor, D.R. (2001) Pricing of CAT Bonds.Google Scholar
Baxter, M. and Rennie, A. (1999) Financial Calculus: An introduction to derivative pricing. Cambridge University Press, U.K.Google Scholar
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, 26–30.Google Scholar
Beirlant, J., Teugels, J. and Vynckier, P. (1996) Practical Analysis of Extreme Value. Leuven University Press, Belgium.Google Scholar
Boyle, P., Broadie, M. and Glasserman, (1997) Monte Carlo methods and security pricing. Journal of Economics 21, 8–9 Google Scholar
Bratley, P., Fox, L.B. and Schrage, E.L. (1987) A Guide to Simulation. Springer, 2nd Edition, U.S.A.CrossRefGoogle Scholar
Briys, E. (1997) From Genoa to Kobe: Natural Hazards, Insurance Risks and the Pricing of Insurance-Linked Bonds. Lehman Brothers International, London U.K.Google Scholar
Coles, S. (2004) An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics, 3rd edition, Great Britain.Google Scholar
Coles, S. (2004) “S-plus Functions for Extreme Value Modeling”. http://www.maths.bris.ac.uk/~masgc/ismev/summary.html.Google Scholar
Cox, H.S. and Pedersen, W.H. (2000) Catastrophe Risk Bonds. N.A.A.J. 4(4), 56–82.Google Scholar
Cummins, D. and Geman, H. (1995) Pricing Catastrophe Futures and Call Spreads: An Arbitrage Approach. Journal of Fixed Income 4, 46–57.CrossRefGoogle Scholar
D’Archy, S.P. and France, G.V. (1992) Catastrophe Futures: A Better Hedge for Insurers. Journal of Risk and Insurance 59, 575–600.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (2003) Modelling Extremal Events. Springer, 4th edition, Germany.Google Scholar
Embrechts, P., Resnick, I.S. and Samorodnitsky, G. (1999) Extreme Value Theory as a Risk Management Tool. N.A.A.J. 3(2), 30–41.Google Scholar
EURIBOR Historical Data (EURIBOR organization): http://www.euribor.org Google Scholar
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, 180–190.CrossRefGoogle Scholar
Gnedenko, B.V. (1943) Sur la distribution limite du terme maximum d’une série alétoire. Annals of Mathematics 44, 423–453.CrossRefGoogle Scholar
Hosking, J.R.M. (1986) Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. Applied Statistics 34, 301–310.CrossRefGoogle Scholar
Institute of Geodynamics, National Observatory of Athens (IG-NOA). At World Wide Web address: http://www.gein.noa.gr/services/cat.html Google Scholar
Jenkinson, A.F. (1969) Statistic of Extremes. Technical Note 98, World Meteorological Organization. Chapter 5, 183–227.Google Scholar
Kellison, G.S. (1991) The Theory of Interest. Irwin/McGraw-Hill. U.S.A.Google Scholar
Kotz, S. and Nadarajah, (2002) Extreme Value Distributions: Theory and Applications. Imperial College Press, Singapore.Google Scholar
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), 25–44.CrossRefGoogle Scholar
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, 125–146.Google Scholar
Macleod, A.J. (1989) Comment on Maximum-Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Applied Statistics 38, 198–199.CrossRefGoogle Scholar
McNeil, J.A. (1997) Estimating the tails of Loss Severity distributions using Extreme Value Theory. ASTIN Bulletin 27(1), 117–137.CrossRefGoogle Scholar
McNeil, J.A. (2001) “EVIS, version 4”. http://www.math.ethz.ch/~mcneil/software.html Google Scholar
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 Google Scholar
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. Google Scholar
O’Brien, T. (1997) Hedging Strategies Using Catastrophe Insurance Options. Insurance: Mathematics and Economics 21, 153–162.Google Scholar
Øksendal, B. (2003) Stochastic Differential Equations. Springer, 6th edition, Germany.CrossRefGoogle Scholar
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, 1563–1566.Google Scholar
Prescott, P. and Walden, A.T. (1980) Maximum Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Biometrika 67, 723–724.CrossRefGoogle Scholar
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, 241–250.CrossRefGoogle Scholar
Resnick, I.S. (1997) Discussion of the Danish Data on Large Fire Insurance Losses. ASTIN Bulletin 27(1), 139–151.CrossRefGoogle Scholar
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).Google Scholar
Romaniuk, M. (2003) Pricing the risk-transfer financial instruments via Monte Carlo methods. System Analysis Modelling Simulation 43(8), 1043–1064.CrossRefGoogle Scholar
United States General Accounting Office (2002) Catastrophe Insurance Risks: The Role of Risk-Linked Securities and Factors Affecting their Use. GAO-02-941. Google Scholar
United States General Accounting Office (2005) Catastrophe Risk: U.S. and European Approaches to Insure Natural Catastrophe and Terrorism Risks. GAO-05-199. Google Scholar
United States General Accounting Office (2006) Federal Emergency Management Agency: Challenges for the National Flood Insurance Program. GAO-06-335T. Google Scholar
Vaugirard, V. (2003) Pricing Catastrophe Bonds by an Arbitrage Approach. The Quarterly Review of Economics and Finance 43, 119–132.CrossRefGoogle Scholar
Vaugirard, V. (2004) A Canonical First Passage Time Model to Pricing Nature-Linked Bonds. Economic Bulletin 7(2), 1–7.Google Scholar
Young, R.V. (2004) Pricing an Incomplete Market with in an Affine Term Structure. Mathematical Finance 14(3), 359–381.CrossRefGoogle Scholar