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Tail Estimation and Catastrophe Security Pricing: Can We Tell What Target We Hit if We Are Shooting in the Dark?

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  • James F. Moore
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    Abstract

    The past few years have seen the development and growth of traded securities with payoffs tied to natural disasters. With this comes a need for tools to evaluate the underlying risks involved. Pricing the insurance features imbedded in these securities is difficult and imprecise. This lack of pricing precision translates into greater required return premiums to holders of these securities This paper explores the nature of pricing uncertainty for a number of data sets, security designs, and loss distributions using mathematical techniques for assessing small-sample variance. Specifically the techniques applied are known as "jackknife" and "bootstrap" and where invented by the statistician John Tukey in the 1950's. The paper contains nearly 50 tables and graphs detailing the findings. Finally, the economic impact of pricing uncertainty is then briefly explored. It is shown that while differences between distribution assumption may not generate statistically significant differences in loss estimates, the economic difference in prices that these different distributions generate is large. The author asserts that while reinsurers will currently place "big bets" based on relatively small amounts of information, it will become more important to develop better understanding of the actual size of these risks as issuers seek to spread them to more entities through the capital markets. He concludes that the more confidently we can state what the price of a risky security "should" be, the more attractive these securities will become and the more successful they will be as investments and means of sharing risk.

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    File URL: http://fic.wharton.upenn.edu/fic/papers/99/9914.pdf
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    Bibliographic Info

    Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 99-14.

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    Date of creation: Mar 1999
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    Handle: RePEc:wop:pennin:99-14

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    1. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
    2. Narayana R. Kocherlakota, 1995. "The equity premium: it's still a puzzle," Discussion Paper / Institute for Empirical Macroeconomics 102, Federal Reserve Bank of Minneapolis.
    3. Kenneth A. Froot & David S. Scharfstein & Jeremy C. Stein, 1992. "Risk Management: Coordinating Corporate Investment and Financing Policies," NBER Working Papers 4084, National Bureau of Economic Research, Inc.
    4. Dwight M. Jaffee & Thomas Russell, 1996. "Catastrophe Insurance, Capital Markets and Uninsurable Risks," Center for Financial Institutions Working Papers 96-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    5. Garven, J. R. & H. Louberge, . "Reinsurance, Taxes and Efficiency: A Contingent Claims Model of Insurance Market Equilibrium," Working Papers 010, Risk and Insurance Archive.
    6. Neil A. Doherty, 1997. "Financial Innovation in the Management of Catastrophe Risk," Journal of Applied Corporate Finance, Morgan Stanley, vol. 10(3), pages 84-95.
    7. Kandel, Shmuel & Stambaugh, Robert F., 1991. "Asset returns and intertemporal preferences," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 39-71, February.
    8. Froot, Kenneth A. & O'Connell, Paul G.J., 2008. "On the pricing of intermediated risks: Theory and application to catastrophe reinsurance," Journal of Banking & Finance, Elsevier, vol. 32(1), pages 69-85, January.
    9. Sara Borden & Asani Sarkar, 1996. "Securitizing property catastrophe risk," Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 2(Aug).
    10. Mayers, David & Smith, Clifford W, Jr, 1990. "On the Corporate Demand for Insurance: Evidence from the Reinsurance Market," The Journal of Business, University of Chicago Press, vol. 63(1), pages 19-40, January.
    11. Neil A. Doherty, 1997. "Financial Innovation in the Management of Catastrophe Risk," Center for Financial Institutions Working Papers 98-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    12. David Cummins & Christopher Lewis & Richard Phillips, 1999. "Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss," NBER Chapters, in: The Financing of Catastrophe Risk, pages 93-148 National Bureau of Economic Research, Inc.
    13. Dong, Weimin & Shah, Haresh & Wong, Felix, 1996. "A Rational Approach to Pricing of Catastrophe Insurance," Journal of Risk and Uncertainty, Springer, vol. 12(2-3), pages 201-18, May.
    14. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-24, July.
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