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An Arbitrage Approach to the Pricing of Catastrophe Options Involving the Cox Process

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  • Fujita, Takahiko
  • Ishimura, Naoyuki
  • Tanaka, Daichi
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    Abstract

    We investigate the valuation and hedging of catastrophe options, whose claim arrival process is modeled by the Cox process or a doubly stochastic Poisson process. Employing the non-arbitrage principle we obtain closed form formula for the pricing of the option. Various hedging parameters are also computed.

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    File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/16521/1/HJeco0490200670.pdf
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    Bibliographic Info

    Article provided by Hitotsubashi University in its journal Hitotsubashi Journal of Economics.

    Volume (Year): 49 (2008)
    Issue (Month): 2 (December)
    Pages: 67-74

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    Handle: RePEc:hit:hitjec:v:49:y:2008:i:2:p:67-74

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    Related research

    Keywords: catastrophe options; Cox process; pricing;

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    1. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. 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.
    3. Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004. "The basis risk of catastrophic-loss index securities," Journal of Financial Economics, Elsevier, vol. 71(1), pages 77-111, January.
    4. Kenneth A. Froot, 1999. "The Market for Catastrophe Risk: A Clinical Examination," NBER Working Papers 7286, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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