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Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach

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  • Perrakis, Stylianos
  • Boloorforoosh, Ali

Abstract

We present a new approach to the pricing of catastrophe event (CAT) derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this approach, we derive values for a CAT option and a reinsurance contract on an insurer’s assets using recent results from the option pricing literature. We show that the assumption of unsystematic event risk seriously underprices the CAT option. Last, we present numerical results for our derivatives using real data from hurricane landings in Florida.

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  • Perrakis, Stylianos & Boloorforoosh, Ali, 2013. "Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3157-3168.
    • Handle: RePEc:eee:jbfina:v:37:y:2013:i:8:p:3157-3168
    DOI: 10.1016/j.jbankfin.2013.02.028
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Perrakis, Stylianos, 1986. "Option Bounds in Discrete Time: Extensions and the Pricing of the American Put," The Journal of Business, University of Chicago Press, vol. 59(1), pages 119-141, January.
    3. Duan, Jin-Chuan & Yu, Min-Teh, 2005. "Fair insurance guaranty premia in the presence of risk-based capital regulations, stochastic interest rate and catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2435-2454, October.
    4. 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.
    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. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
    7. 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(1), pages 93-115, March.
    8. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
    9. Perrakis, Stylianos & Ryan, Peter J, 1984. "Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-525, June.
    10. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277.
    11. Pauline Barrieu & Henri Loubergé, 2009. "Hybrid Cat Bonds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 547-578, September.
    12. 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.
    13. Lin, X. Sheldon & Wang, Tao, 2009. "Pricing perpetual American catastrophe put options: A penalty function approach," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 287-295, April.
    14. Ritchken, Peter H & Kuo, Shyanjaw, 1988. " Option Bounds with Finite Revision Opportunities," Journal of Finance, American Finance Association, vol. 43(2), pages 301-308, June.
    15. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    16. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    17. Amin, Kaushik I & Ng, Victor K, 1993. "Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
    18. Constantinides, George M. & Perrakis, Stylianos, 2002. "Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1323-1352, July.
    19. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2011. "Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence," Journal of Finance, American Finance Association, vol. 66(4), pages 1407-1437, August.
    20. 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.
    21. 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.
    22. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March.
    23. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
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    Cited by:

    1. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    2. Hamed Ghanbari & Michael Oancea & Stylianos Perrakis, 2021. "Shedding light on a dark matter: Jump diffusion and option‐implied investor preferences," European Financial Management, European Financial Management Association, vol. 27(2), pages 244-286, March.
    3. Stylianos Perrakis & Ali Boloorforoosh, 2018. "Catastrophe futures and reinsurance contracts: An incomplete markets approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(1), pages 104-128, January.
    4. Denis-Alexandre Trottier & Van Son Lai & Anne-Sophie Charest, 2017. "CAT Bond Spreads Via HARA Utility and Nonparametric Tests," Working Papers 2017-002, Department of Research, Ipag Business School.
    5. Denis-Alexandre Trottier & Van Son Lai, 2017. "Reinsurance or CAT Bond? How to Optimally Combine Both," Working Papers 2017-003, Department of Research, Ipag Business School.
    6. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A General Class of Distortion Operators for Pricing Contingent Claims with Applications to CAT Bonds," Working Papers 2019-004, Department of Research, Ipag Business School.

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    More about this item

    Keywords

    Catastrophe events; Jump processes; Jump-diffusion; Insurance products; Derivative assets;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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