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Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds

Published online by Cambridge University Press:  09 August 2013

Gareth G. Haslip  and
Vladimir K. Kaishev
Gareth G. Haslip
Affiliation:
Sir John Cass Business School, City University, 106 Bunhill Road, London EC1Y 8TZ, Tel.: +44 (0)789 1691 811, E-Mail: [email protected]
Vladimir K. Kaishev
Affiliation:
Sir John Cass Business School, City University, 106 Bunhill Road, London EC1Y 8TZ, Tel.: +44 (0)20 7040 8453, E-Mail: [email protected]
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Abstract

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process.

Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered.

The methodology is illustrated on several examples including Pareto and Gamma claim severities.

Keywords

Reinsurancecatastrophe bondsrisk neutral valuationsecuritisationFast Fourier TransformFractional Fast Fourier Transform
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 307 - 329
Copyright
Copyright © International Actuarial Association 2010

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References

Aon Benfield Securities (2009) Insurance-Linked Securities Adapting to an Evolving Market 2009. Aon Benfield Securities Limited.Google Scholar
Bailey, D.H. and Swarztrauber, P.N. (1990) The Fractional Fourier Transform and Applications, NAS System Division. NASA Ames Research Center.Google Scholar
Baryshnikov, Y., Mayo, A. and Taylor, D.R. (2001) Pricing of CAT Bonds. Working paper.Google Scholar
Baxter, M.W. and Rennie, A.J.O. (1996) Financial Calculus: An Introduction to Derivative Pricing. Press Syndicate of the University of Cambridge.CrossRefGoogle Scholar
Bottazzi, G. (2007) On the Pareto Type III distribution. Laboratory of Economics and Management (LEM) Sant'Anna School of Advanced Studies, Pisa, Italy.Google Scholar
Burnecki, K., Kukla, G. and Taylor, D. (2005) Pricing of catastrophe bonds. Statistical Tools for Finance and Insurance, Springer, Berlin.Google Scholar
Burnecki, K. (2005) Pricing catastrophe bonds in a compound non-homogeneous Poisson model with left-truncated loss distributions. Mathematics in Finance Conference, Berg-en-Dal.Google Scholar
Calvetti, D., Golub, G.H., Gragg, W.B. and Reichel, L. (2000) Computation of Gauss-Kronrod Quadrature Rules. Math. Comput. 69, 1035–1052.CrossRefGoogle Scholar
Carr, P. and Madan, D. (1999) Option Valuation Using Fast Fourier Transform. Journal of Computational Finance 2(4), 61–73.CrossRefGoogle Scholar
Chourdakis, K. (2005) Option Pricing Using the Fractional FFT. Journal of Computational Finance 8(2), 1–18.CrossRefGoogle Scholar
Cont, R. and Tankov, P. (2004) Financial Modelling With Jump Processes. Chapman and Hall/CRC Financial Mathematics Series.Google Scholar
Delbaen, F. and Haezendonck, J. (1989) A Martingale Approach to Premium Calculation Principles in an Arbitrage Free Market. Insurance: Mathematics and Economics 8, 269–277.Google Scholar
Delbaen, F. and Schachermayer, W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463–520.CrossRefGoogle Scholar
Dufresne, D., Garrido, J. and Morales, M. (2006) Fourier Inversion Formula Option Pricing and Insurance. Methodology and Computing In Applied Probability, 11(3), 359–383.CrossRefGoogle Scholar
Embrechts, P. (1996) Actuarial versus financial pricing of insurance. Risk Finance 1(4), 17–26.CrossRefGoogle Scholar
Holtan, J. (2004) Pragmatic Insurance Pricing, XXXVth ASTIN Colloquium.Google Scholar
The Insurance Insider (2007), Executive Briefing Autumn 2007, www.insuranceinsider.com Google Scholar
Insurance Journal Property and Casualty Magazine (2002) Merrill Lynch Forms Bermuda Reinsurance Co., Wells Publishing, http://www.insurancejournal.com/news/international/2002/06/06/16283.htm. Google Scholar
Jaimungal, S., Jackson, K.R., and Surkov, V. (2007) Option Pricing with Regime Switching Lévy Processes using Fourier Space Time-stepping. Proceeding of the Fourth IASTED International Conference on Financial Engineering and Applications, 92–97, 2007.Google Scholar
Lewis, A.L. (2001) A simple option formula for general jump-diffusion and other exponential Lévy processes. Envision Financial Systems and Option City.net.CrossRefGoogle Scholar
McGhee, C., Clarke, R., Fugit, J. and Hathaway, J. (2007) The Catastrophe Bond Market at Year-End 2007: The Market Goes Mainstream. Investment Banking Speciality Practice, MMC Securities Corp.Google Scholar
McGhee, C., Clarke, R., and Collura, J. (2006) The Catastrophe Bond Market at Year-End 2006. Investment Banking Speciality Practice, MMC Securities Corp.Google Scholar
Muermann, A. (2002) Actuarially Consistent Valuation in an Integrated Market. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.Google Scholar
Muermann, A. (2003) Actuarially Consistent Valuation of Catastrophe Derivatives. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.Google Scholar
Muermann, A. (2006) Market Price of Insurance Risk Implied by Catastrophe Derivatives. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.Google Scholar
Press, W.H., Flannery, P.F., Teukolsky, S.A. and Vetterling, W.T. (1988) Numerical Recipes in C: The Art of Scientific Computing. Press Syndicate of the University of Cambridge.Google Scholar
Schoutens, W. (2003) Levy Processes in Finance: Pricing Financial Derivatives, Wiley, New York, 2003.CrossRefGoogle Scholar
Sondermann, D. (1991) Reinsurance in arbitrage-free markets. Insurance: Mathematics and Economics 10, 191–202.Google Scholar
Wacek, M.G. (1997) Application of the Option Market Paradigm to the Solution of Insurance Problems. Proceedings of the Casualty Actuarial Society LXXXIV, 701–733.Google Scholar
Weir, A.J. (1973) Lebesgue Integration and Measure. Press Syndicate of the University of Cambridge.CrossRefGoogle Scholar
Young, V.R. (2004) Encyclopedia of Actuarial Science. Wiley.Google Scholar