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Catastrophe equity put options with target variance


  • Wang, Xingchun


In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.

Suggested Citation

  • Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
  • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:79-86 DOI: 10.1016/j.insmatheco.2016.08.010

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    References listed on IDEAS

    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Hoi Ying Wong & Jing Zhao, 2010. "Currency option pricing: Mean reversion and multi‐scale stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(10), pages 938-956, October.
    3. 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.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    5. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    6. Xingchun Wang, 2016. "The Pricing of Catastrophe Equity Put Options with Default Risk," International Review of Finance, International Review of Finance Ltd., vol. 16(2), pages 181-201, June.
    7. 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.
    8. Charles Levi, 1 & Partrat, Christian, 1991. "Statistical Analysis of Natural Events in the United States," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(02), pages 253-276, November.
    9. Robert Jarrow & Younes Kchia & Martin Larsson & Philip Protter, 2013. "Discretely sampled variance and volatility swaps versus their continuous approximations," Finance and Stochastics, Springer, vol. 17(2), pages 305-324, April.
    10. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    11. Chia‐Chien Chang & Shih‐Kuei Lin & Min‐Teh Yu, 2011. "Valuation of Catastrophe Equity Puts With Markov‐Modulated Poisson Processes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 447-473, June.
    12. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    13. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, pages 327-343.
    15. Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, October.
    16. 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.
    17. Jiang, I-Ming & Yang, Sheng-Yung & Liu, Yu-Hong & Wang, Alan T., 2013. "Valuation of double trigger catastrophe options with counterparty risk," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 226-242.
    18. 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.
    19. Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Rare Shock, Two-Factor Stochastic Volatility and Currency Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, pages 32-50.
    20. Wendong Zheng & Yue Kuen Kwok, 2014. "Closed Form Pricing Formulas For Discretely Sampled Generalized Variance Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 855-881, October.
    21. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.
    22. Duan, Jin-Chuan & Simonato, Jean-Guy, 2002. "Maximum likelihood estimation of deposit insurance value with interest rate risk," Journal of Empirical Finance, Elsevier, pages 109-132.
    23. Lin, Shih-Kuei & Chang, Chia-Chien & Powers, Michael R., 2009. "The valuation of contingent capital with catastrophe risks," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 65-73, August.
    24. Chang, Lung-fu & Hung, Mao-wei, 2009. "Analytical valuation of catastrophe equity options with negative exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 59-69, February.
    25. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
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    1. repec:eee:phsmap:v:485:y:2017:i:c:p:91-103 is not listed on IDEAS

    More about this item


    Catastrophe equity put options; Realized variance; Realized volatility; Catastrophic events; Doubly stochastic Poisson processes;

    JEL classification:

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


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