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

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  • Fujita, Takahiko
  • 藤田, 岳彦
  • Ishimura, Naoyuki
  • 石村, 直之
  • 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 & 藤田, 岳彦 & Ishimura, Naoyuki & 石村, 直之 & 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
    DOI: 10.15057/16521
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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. 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.
    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. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. 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.

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    More about this item

    Keywords

    catastrophe options; Cox process; pricing;
    All these keywords.

    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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