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Valuing catastrophe bonds by Monte Carlo simulations

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  • Victor Vaugirard

Abstract

This paper reports fairly accurate simulations of insurance-linked securities within an arbitrage-free framework, while accounting for catastrophic events and allowing for stochastic interest rates. Assessing these contingent claims exhibits features of instability rooted in the discontinuity of the payoffs of binary options around their threshold, which is magnified by possible jumps in their underlying dynamics. The error made while simulating path-dependent digital options whose underlyings obey geometric Brownian motion is used to control the estimation of digital options whose underlyings follow jump-diffusion processes. Comparative statics results highlight the hump shape of the term structure of catbond yield spreads.

Suggested Citation

  • Victor Vaugirard, 2003. "Valuing catastrophe bonds by Monte Carlo simulations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 75-90.
    • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:75-90
    DOI: 10.1080/1350486032000079741
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    References listed on IDEAS

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    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Dietmar P. J. Leisen, 1999. "Valuation of Barrier Options in a Black-Scholes Setup with Jump Risk," Computing in Economics and Finance 1999 133, Society for Computational Economics.
    3. Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    5. Michael S. Canter & Joseph B. Cole & Richard L. Sandor, 1997. "Insurance Derivatives: A New Asset Class for the Capital Markets and a New Hedging Tool for the Insurance Industry," Journal of Applied Corporate Finance, Morgan Stanley, vol. 10(3), pages 69-81, September.
    6. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    7. Patrice Poncet & Victor Vaugirard, 2001. "The valuation of nature-linked bonds with exchange rate risk," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 25(3), pages 293-307, September.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. 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.
    10. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    11. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    12. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
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    Cited by:

    1. Lai, Van Son & Parcollet, Mathieu & Lamond, Bernard F., 2014. "The valuation of catastrophe bonds with exposure to currency exchange risk," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 243-252.
    2. Fabio Pizzutilo & Elisabetta Venezia, 2018. "Are catastrophe bonds effective financial instruments in the transport and infrastructure industries? Evidence from international financial markets," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(2), pages 256-267, April.
    3. 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.
    4. Peter Carayannopoulos & Olga Kanj & M. Fabricio Perez, 2022. "Pricing dynamics in the market for catastrophe bonds," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 172-202, January.
    5. 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.
    6. Lev Eppelbaum, 2013. "Non-stochastic long-term prediction model for US tornado level," 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. 69(3), pages 2269-2278, December.
    7. Ben Ammar, Semir & Braun, Alexander & Eling, Martin, 2015. "Alternative Risk Transfer and Insurance-Linked Securities: Trends, Challenges and New Market Opportunities," I.VW HSG Schriftenreihe, University of St.Gallen, Institute of Insurance Economics (I.VW-HSG), volume 56, number 56.
    8. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
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