IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v10y2003i1p75-90.html
   My bibliography  Save this article

Valuing catastrophe bonds by Monte Carlo simulations

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000079741
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. 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.
    6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    9. 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.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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, May.
    7. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    8. repec:dau:papers:123456789/1483 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    3. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. Lee, Jin-Ping & Yu, Min-Teh, 2007. "Valuation of catastrophe reinsurance with catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 264-278, September.
    5. Kent Wang & Yuqiang Guo, 2014. "Predictability of time-varying jump premiums: Evidence based on calibration," Australian Journal of Management, Australian School of Business, vol. 39(3), pages 369-394, August.
    6. repec:wyi:journl:002192 is not listed on IDEAS
    7. 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.
    8. Victor Vaugirard, 2004. "A canonical first passage time model to pricing nature-linked bonds," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-7.
    9. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    10. Chenghu Ma, 2003. "Term Structure of Interest Rates in the Presence of Levy Jumps: The HJM Approach," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 401-426, November.
    11. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    12. Peña Sánchez de Rivera, Juan Ignacio & Moreno, Manuel, 1995. "On the term structure of Interbank interest rates: jump-diffusion processes and option pricing," DES - Working Papers. Statistics and Econometrics. WS 7074, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    14. Stephan Dieckmann & Michael Gallmeyer, 2006. "Pricing Rare Event Risk in Emerging Markets," 2006 Meeting Papers 305, Society for Economic Dynamics.
    15. repec:ebl:ecbull:v:7:y:2004:i:2:p:1-7 is not listed on IDEAS
    16. repec:dau:papers:123456789/5374 is not listed on IDEAS
    17. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    18. Prabakaran, Sellamuthu & Garcia, Isabel C. & Mora, Jose U., 2020. "A temperature stochastic model for option pricing and its impacts on the electricity market," Economic Analysis and Policy, Elsevier, vol. 68(C), pages 58-77.
    19. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    20. Willi Semmler, 2011. "Asset Prices, Booms and Recessions," Springer Books, Springer, number 978-3-642-20680-1, March.
    21. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2010, November.
    22. Laura Ballotta & Ioannis Kyriakou, 2015. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 115-129, January.
    23. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 15, July-Dece.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:75-90. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.