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

Author

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

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.

Suggested Citation

  • Fujita, Takahiko & Ishimura, Naoyuki & Tanaka, Daichi, 2008. "An Arbitrage Approach to the Pricing of Catastrophe Options Involving the Cox Process," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 49(2), pages 67-74, December.
  • Handle: RePEc:hit:hitjec:v:49:y:2008:i:2:p:67-74
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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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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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. 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.
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    Citations

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    Cited by:

    1. Gunther Leobacher & Philip Ngare, 2014. "Utility indifference pricing of derivatives written on industrial loss indexes," Papers 1404.0879, arXiv.org.
    2. Andreas Eichler & Gunther Leobacher & Michaela Szolgyenyi, 2016. "Utility Indifference Pricing of Insurance Catastrophe Derivatives," Papers 1607.01110, arXiv.org, revised May 2017.

    More about this item

    Keywords

    catastrophe options; Cox process; pricing;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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