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Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds

  • Gareth G. Haslip (a1) and Vladimir K. Kaishev (a2)
Abstract
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.

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References
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Aon Benfield Securities (2009) Insurance-Linked Securities Adapting to an Evolving Market 2009. Aon Benfield Securities Limited.
Bailey D.H. and Swarztrauber P.N. (1990) The Fractional Fourier Transform and Applications, NAS System Division. NASA Ames Research Center.
Baryshnikov Y., Mayo A. and Taylor D.R. (2001) Pricing of CAT Bonds. Working paper.
Baxter M.W. and Rennie A.J.O. (1996) Financial Calculus: An Introduction to Derivative Pricing. Press Syndicate of the University of Cambridge.
Bottazzi G. (2007) On the Pareto Type III distribution. Laboratory of Economics and Management (LEM) Sant'Anna School of Advanced Studies, Pisa, Italy.
Burnecki K., Kukla G. and Taylor D. (2005) Pricing of catastrophe bonds. Statistical Tools for Finance and Insurance, Springer, Berlin.
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.
Calvetti D., Golub G.H., Gragg W.B. and Reichel L. (2000) Computation of Gauss-Kronrod Quadrature Rules. Math. Comput. 69, 10351052.
Carr P. and Madan D. (1999) Option Valuation Using Fast Fourier Transform. Journal of Computational Finance 2(4), 6173.
Chourdakis K. (2005) Option Pricing Using the Fractional FFT. Journal of Computational Finance 8(2), 118.
Cont R. and Tankov P. (2004) Financial Modelling With Jump Processes. Chapman and Hall/CRC Financial Mathematics Series.
Delbaen F. and Haezendonck J. (1989) A Martingale Approach to Premium Calculation Principles in an Arbitrage Free Market. Insurance: Mathematics and Economics 8, 269277.
Delbaen F. and Schachermayer W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463520.
Dufresne D., Garrido J. and Morales M. (2006) Fourier Inversion Formula Option Pricing and Insurance. Methodology and Computing In Applied Probability, 11(3), 359383.
Embrechts P. (1996) Actuarial versus financial pricing of insurance. Risk Finance 1(4), 1726.
Holtan J. (2004) Pragmatic Insurance Pricing, XXXVth ASTIN Colloquium.
The Insurance Insider (2007), Executive Briefing Autumn 2007, www.insuranceinsider.com
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.
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, 9297, 2007.
Lewis A.L. (2001) A simple option formula for general jump-diffusion and other exponential Lévy processes. Envision Financial Systems and Option City.net.
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.
McGhee C., Clarke R., and Collura J. (2006) The Catastrophe Bond Market at Year-End 2006. Investment Banking Speciality Practice, MMC Securities Corp.
Muermann A. (2002) Actuarially Consistent Valuation in an Integrated Market. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.
Muermann A. (2003) Actuarially Consistent Valuation of Catastrophe Derivatives. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.
Muermann A. (2006) Market Price of Insurance Risk Implied by Catastrophe Derivatives. Working Paper, Financial Institutions Center, The Wharton School, University of Pennsylvania.
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.
Schoutens W. (2003) Levy Processes in Finance: Pricing Financial Derivatives, Wiley, New York, 2003.
Sondermann D. (1991) Reinsurance in arbitrage-free markets. Insurance: Mathematics and Economics 10, 191202.
Wacek M.G. (1997) Application of the Option Market Paradigm to the Solution of Insurance Problems. Proceedings of the Casualty Actuarial Society LXXXIV, 701733.
Weir A.J. (1973) Lebesgue Integration and Measure. Press Syndicate of the University of Cambridge.
Young V.R. (2004) Encyclopedia of Actuarial Science. Wiley.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
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