IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v49y2011i3p520-536.html
   My bibliography  Save this article

Pricing catastrophe swaps: A contingent claims approach

Author

Listed:
  • Braun, Alexander

Abstract

In this paper, we comprehensively analyze the catastrophe (cat) swap, a financial instrument which has attracted little scholarly attention to date. We begin with a discussion of the typical contract design, the current state of the market, as well as major areas of application. Subsequently, a two-stage contingent claims pricing approach is proposed, which distinguishes between the main risk drivers ex-ante as well as during the loss reestimation phase and additionally incorporates counterparty default risk. Catastrophe occurrence is modeled as a doubly stochastic Poisson process (Cox process) with mean-reverting Ornstein–Uhlenbeck intensity. In addition, we fit various parametric distributions to normalized historical loss data for hurricanes and earthquakes in the US and find the heavy-tailed Burr distribution to be the most adequate representation for loss severities. Applying our pricing model to market quotes for hurricane and earthquake contracts, we derive implied Poisson intensities which are subsequently condensed into a common factor for each peril by means of exploratory factor analysis. Further examining the resulting factor scores, we show that a first order autoregressive process provides a good fit. Hence, its continuous-time limit, the Ornstein–Uhlenbeck process should be well suited to represent the dynamics of the Poisson intensity in a cat swap pricing model.

Suggested Citation

  • Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:520-536
    DOI: 10.1016/j.insmatheco.2011.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711000849
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk-Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545.
    3. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    4. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2004. "Valuation of structured risk management products," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 259-272, April.
    5. Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
    6. 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.
    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    8. Knut Aase, 1999. "An Equilibrium Model of Catastrophe Insurance Futures and Spreads," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 69-96, June.
    9. Houweling, Patrick & Vorst, Ton, 2005. "Pricing default swaps: Empirical evidence," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1200-1225, December.
    10. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381.
    11. Bakshi, Gurdip & Madan, Dilip, 2002. "Average Rate Claims with Emphasis on Catastrophe Loss Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 93-115, March.
    12. Victor Vaugirard, 2004. "A canonical first passage time model to pricing nature-linked bonds," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-7.
    13. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515 World Scientific Publishing Co. Pte. Ltd..
    14. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 297-302, October.
    15. Balbás, Alejandro & Longarela, Iñaki R. & Lucia, Julio J., 1999. "How does financial theory apply to catastrophe-linked derivatives? En empirical test of several princing models," DEE - Working Papers. Business Economics. WB 6521, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    16. John Y. Campbell & John H. Cochrane, 1994. "By force of habit: a consumption-based explanation of aggregate stock market behavior," Working Papers 94-17, Federal Reserve Bank of Philadelphia.
    17. Charles Levi, 1 & Partrat, Christian, 1991. "Statistical Analysis of Natural Events in the United States," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(02), pages 253-276, November.
    18. Sara Borden & Asani Sarkar, 1996. "Securitizing property catastrophe risk," Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 2(Aug).
    19. repec:fth:geneec:99.01 is not listed on IDEAS
    20. 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.
    21. Robert E. Hoyt & Kathleen A. McCullough, 1999. "Catastrophe Insurance Options: Are They Zero-Beta Assets?," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 147-163.
    22. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    23. 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: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    24. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    25. Christensen, Claus Vorm & Schmidli, Hanspeter, 2000. "Pricing catastrophe insurance products based on actually reported claims," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 189-200, October.
    26. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    27. 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.
    28. Stanley Mutenga & Sotiris K Staikouras, 2007. "The Theory of Catastrophe Risk Financing: A Look at the Instruments that Might Transform the Insurance Industry," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 32(2), pages 222-245, April.
    29. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    30. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeLi, 2010. "Pricing catastrophe options with stochastic claim arrival intensity in claim time," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 24-32, January.
    31. repec:ebl:ecbull:v:7:y:2004:i:2:p:1-7 is not listed on IDEAS
    32. Lane, Morton N., 2000. "Pricing Risk Transfer Transactions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(02), pages 259-293, November.
    33. Milidonis, Andreas & Grace, Martin F., 2008. "Tax-Deductible Pre-Event Catastrophe Loss Reserves: The Case of Florida," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(01), pages 13-51, May.
    34. 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.
    35. 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.
    36. Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, October.
    37. 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.
    38. Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 469-483, June.
    39. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," LSE Research Online Documents on Economics 16375, London School of Economics and Political Science, LSE Library.
    40. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeiLi, 2008. "Pricing catastrophe options in discrete operational time," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 422-430, December.
    41. Robert W. Klein & Shaun Wang, 2009. "Catastrophe Risk Financing in the United States and the European Union: A Comparative Analysis of Alternative Regulatory Approaches," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 607-637.
    42. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
    43. Javier Gil-Bazo, 2006. "The value of the 'swap' feature in equity default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 67-74.
    44. Victor Vaugirard, 2003. "Valuing catastrophe bonds by Monte Carlo simulations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 75-90.
    45. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
    46. Henri Louberge & Evis Kellezi & Manfred Gilli, 1999. "Using Catastrophe-Linked Securities to Diversity Insurance Risk: A Financial Analysis of Cat Bonds," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 125-146.
    47. Lane, Morton & Mahul, Olivier, 2008. "Catastrophe risk pricing : an empirical analysis," Policy Research Working Paper Series 4765, The World Bank.
    48. 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.
    49. Henry Kaiser, 1974. "An index of factorial simplicity," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 31-36, March.
    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. Massimo Mariani & Paola Amoruso, 2016. "The Effectiveness of Catastrophe Bonds in Portfolio Diversification," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1760-1767.
    2. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    3. Ben Ammar, Semir & Braun, Alexander & Eling, Martin, 2016. "Asset Pricing and Extreme Event Risk: Common Factors in ILS Fund Returns," Working Papers on Finance 1621, University of St. Gallen, School of Finance.
    4. repec:bla:jrinsu:v:83:y:2016:i:4:p:811-847 is not listed on IDEAS
    5. Xingchun Wang, 2016. "The Pricing of Catastrophe Equity Put Options with Default Risk," International Review of Finance, International Review of Finance Ltd., vol. 16(2), pages 181-201, June.
    6. repec:gam:jrisks:v:5:y:2017:i:4:p:64-:d:123183 is not listed on IDEAS
    7. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.

    More about this item

    Keywords

    Catastrophe swaps; Contingent claims pricing approach; Doubly stochastic Poisson process; Mean-reverting Ornstein–Uhlenbeck intensity; Counterparty default risk; Implied intensities; Exploratory factor analysis; First order autoregressive process;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:eee:insuma:v:49:y:2011:i:3:p:520-536. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.