Abstract
This paper examines the impact of the 2005 hurricane season, particularly Hurricane Katrina, on the pricing of CAT bonds. We examine whether highly rated CAT bonds demonstrate a different relationship than subinvestment bonds between objective risk measures and the spread. The theoretical framework for this relationship is based on the Lance Financial (LFC) model, introduced by Lane (Rationale and results with the LFC cat bond pricing model, Discussion paper, Lane Financial LLC, Wilmette, 2003). The empirical results of treed Bayesian estimation confirm that the severity component of the spread has an increased impact, indicating a shift in investor perception during the pricing process. The impact of the conditional expected loss also significantly increases, but it contributes through its interaction with the attachment probability rather than through its variance. Finally, we show that the influence of conditional expected loss is also increased by investment-grade ratings, because investors who demand highly rated bonds may be more concerned about possible losses than junk bond investors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bantwal, V.J., Kunreuther, H.C.: A cat bond premium puzzle? J. Psychol. Financ. Markets 1(1), 76–91 (2000)
Best, A.M.: Rating Natural Catastrophe Bonds. A.M. Best’s Quick Reference. http://www.ambest.com/ratings/methodology/QuickRef-CatBonds.pdf January (2008)
Chipman, H.A., George, E.I., McCulloch, R.E.: Bayesian CART model search. J. Am. Stat. Assoc. 93(443), 935–960 (1998)
Chipman, H.A., George, E.I., McCulloch, R.E.: Bayesian treed models. Mach. Learn. 48, 299–320 (2002)
Cox, S.H., Pederson, H.W.: Catastrophe risk bonds. N. Am. Actuarial J. 4(4), 56–82 (2000)
Cummins, D.J.: CAT bonds and other risk-linked securities: state of the market and recent developments. Risk Manag. Insur. Rev. 11(1), 23–47 (2008)
Egami, M., Young, V.R.: Indifference prices of structured catastrophe (CAT) bonds. Insur. Math. Econ. 42(2), 771–778 (2008)
Froot, K.A., Murphy, B., Stern, A., Usher, S.: The emerging asset class: insurance risk. Special Report from Guy Carpenter and Company, Inc. Reprinted in Viewpoint 24(3), 19–28. http://www.nber.org/reporter/summer99/froot.html (July 1995)
Gramacy, R.B.: tgp: an R package for Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian process models. J. Stat. Software 19(9), 1–46 (2007)
Gramacy, R.B., Lee, H.K.H.: Bayesian treed Gaussian process models with an application to computer modeling. J. Am. Stat. Assoc. 103(483), 1119–1130 (2008)
Kleindorfer, P.R., Kunreuther, H.C.: Challenges facing the insurance industry in managing catastrophic risks. In: Froot. K.A. (ed.) The Financing of Catastrophe Risk, A National Bureau of Economic Research Project Report, University of Chicago Press, pp. 149–194 (1999)
Kull, A.: A unifying approach to pricing insurance and financial risk. Casualty Actuarial Society (ed.) Winter forum 2003, data management, quality, and technology call papers and ratemaking discussion papers, Arlington, pp. 317–350 (2003)
Lane, M.N.: Rationale and results with the LFC cat bond pricing model. Discussion paper, Lane Financial LLC, Wilmette (2003)
Lane, M.N.: Over the top, but not off the boil. Discussion paper, Lane Financial LLC, Wilmette (2006)
Lane, M.N.: What were we thinking? Discussion paper, Lane Financial LLC, Wilmette (2008)
Lane, M.N., Beckwith, R.G.: How high is up?: the 2006 review of the insurance securitization market. Discussion paper, Lane Financial LLC, Wilmette (2006)
Lane, M.N., Beckwith, R.G.: The 2008 review of ILS transaction – what price ILS?: a work in progress. Discussion paper, Lane Financial LLC, Wilmette (2008)
Lane, M.N., Mahul, O.: Catastrophe Risk Pricing: An Empirical Analysis. Policy Research Working Paper, vol. 4765. The World Bank, Washington, DC (2008)
Munich Re: Zwischen Hoch und Tief: Wetterrisiken in Mitteleuropa. Discussion paper, Munich (2007)
Saltelli, A.: Making best use of model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145, 280–297 (2002)
Slovic, P.: Perception of risk. Science 236, 280–285 (1987)
Tilley, J.A.: The Securitization of Catastrophic Property Risks in ASTIN/AFIR. Colloquia. International Actuarial Association ed., Cairns (1997)
Wang, S.S.: CAT bond pricing using probability transforms. The Geneva Papers on Risk and Insurance: Études et Dossiers, vol. 278, pp. 19–29 (2004)
Zweifel, P., Eisen, R.: Versicherungsökonomie: Mit 65 Tabellen. Springer, Berlin (2003)
Acknowledgements
The authors are grateful to the Department of Empirical Research and Applied Econometrics at Albert Ludwigs University Freiburg, Germany for the support received during completion of this study and Willis, U.K. for enabling us the dataset and for the permission to use it for academical purposes.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ahrens, F., Füss, R., Selcuk-Kestel, A.S. (2014). A Bayesian Pricing Model for CAT Bonds. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04849-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-04849-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04848-2
Online ISBN: 978-3-319-04849-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)