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Pricing and simulating catastrophe risk bonds in a Markov-dependent environment

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  • Shao, Jia
  • Papaioannou, Apostolos D.
  • Pantelous, Athanasios A.

Abstract

At present, insurance companies are seeking more adequate liquidity funds to cover the insured property losses related to natural and manmade disasters. Past experience shows that the losses caused by catastrophic events, such as earthquakes, tsunamis, floods, or hurricanes, are extremely high. An alternative method for covering these extreme losses is to transfer part of the risk to the financial markets by issuing catastrophe-linked bonds. In this paper, we propose a contingent claim model for pricing catastrophe risk bonds (CAT bonds). First, using a two-dimensional semi-Markov process, we derive analytical bond pricing formulae in a stochastic interest rate environment with aggregate claims that follow compound forms, where the claim inter-arrival times are dependent on the claim sizes. Furthermore, we obtain explicit CAT bond prices formulae in terms of four different payoff functions. Next, we estimate and calibrate the parameters of the pricing models using catastrophe loss data provided by Property Claim Services from 1985 to 2013. Finally, we use Monte Carlo simulations to analyse the numerical results obtained with the CAT bond pricing formulae.

Suggested Citation

  • Shao, Jia & Papaioannou, Apostolos D. & Pantelous, Athanasios A., 2017. "Pricing and simulating catastrophe risk bonds in a Markov-dependent environment," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 68-84.
  • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:68-84
    DOI: 10.1016/j.amc.2017.03.041
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    as
    1. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Tse,Yiu-Kuen, 2009. "Nonlife Actuarial Models," Cambridge Books, Cambridge University Press, number 9780521764650, December.
    5. Kenneth A. Froot & Steven E. Posner, 2002. "The Pricing of Event Risks with Parameter Uncertainty," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(2), pages 153-165, December.
    6. Lin, X. Sheldon & Wang, Tao, 2009. "Pricing perpetual American catastrophe put options: A penalty function approach," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 287-295, April.
    7. Reinhard, Jean-Marie, 1984. "On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 23-43, April.
    8. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    9. N. Karagiannis & H. Assa & A. A. Pantelous & C. G. Turvey, 2016. "Modelling and pricing of catastrophe risk bonds with a temperature-based agricultural application," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1949-1959, December.
    10. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    11. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381, July.
    12. Janssen, Jacques, 1980. "Some Transient Results on the M/SM/1 Special Semi-Markov Model in Risk and Queueing Theories," ASTIN Bulletin, Cambridge University Press, vol. 11(1), pages 41-51, June.
    13. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    14. Vaugirard, Victor E., 2003. "Pricing catastrophe bonds by an arbitrage approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(1), pages 119-132.
    15. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    16. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    17. Härdle, Wolfgang Karl & Cabrera, Brenda López, 2007. "Calibrating CAT bonds for Mexican earthquakes," SFB 649 Discussion Papers 2007-037, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    18. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    19. Asmussen, Soren & Rolski, Tomasz, 1992. "Computational methods in risk theory: A matrix-algorithmic approach," Insurance: Mathematics and Economics, Elsevier, vol. 10(4), pages 259-274, January.
    20. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    21. Sebastian Jaimungal & Yuxiang Chong, 2014. "Valuing clustering in catastrophe derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 259-270, February.
    22. Siegl, Thomas & Tichy, Robert F., 1999. "A process with stochastic claim frequency and a linear dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 51-65, March.
    23. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    24. Egami, Masahiko & Young, Virginia R., 2008. "Indifference prices of structured catastrophe (CAT) bonds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 771-778, April.
    25. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2000. "Economic Aspects of Securitization of Risk," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 157-193, May.
    26. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    27. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    28. Zimbidis, Alexandros A. & Frangos, Nickolaos E. & Pantelous, Athanasios A., 2007. "Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 163-183, May.
    29. Samuel Cox & Hal Pedersen, 2000. "Catastrophe Risk Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 56-82.
    30. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    31. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
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    6. Harsh K. Mistry & Domenico Lombardi, 2023. "A stochastic exposure model for seismic risk assessment and pricing of catastrophe bonds," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 117(1), pages 803-829, May.
    7. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2023. "How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework," Sustainability, MDPI, vol. 15(9), pages 1-19, May.
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