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Valuation of new-designed contracts for catastrophe risk management

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  • Wang, Xingchun

Abstract

In this study, we design and price a new kind of catastrophe equity put options, whose payoff depends on the ratio of accumulated losses and the expected level over the life of the option. We adopt a compound Poisson process to describe accumulated catastrophe losses and assume catastrophe losses affect the prices of the underlying stock. In the proposed framework, we obtain an explicit pricing formula of the new kind of catastrophe equity put options. Finally, numerical results are presented to investigate the values of this new class of options and illustrate the differences between the prices of vanilla catastrophe equity put options and the contracts designed in this paper. Interestingly, the prices of the new-designed contracts with different power exponents change oppositely as the intensity rises.

Suggested Citation

  • Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    • Handle: RePEc:eee:ecofin:v:50:y:2019:i:c:s1062940819301032
    DOI: 10.1016/j.najef.2019.101041
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    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. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    3. 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.
    4. 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.
    5. Xu, Guangli & Shao, Xinjian & Wang, Xingchun, 2019. "Analytical valuation of power exchange options with default risk," Finance Research Letters, Elsevier, vol. 28(C), pages 265-274.
    6. Bi, Hongwei & Wang, Guanying & Wang, Xingchun, 2019. "Valuation of catastrophe equity put options with correlated default risk and jump risk," Finance Research Letters, Elsevier, vol. 29(C), pages 323-329.
    7. Xingchun Wang & Shiyu Song & Yongjin Wang, 2017. "The Valuation of Power Exchange Options with Counterparty Risk and Jump Risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(5), pages 499-521, May.
    8. 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.
    9. 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.
    10. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
    11. Xingchun Wang, 2017. "Differences in the Prices of Vulnerable Options with Different Counterparties," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(2), pages 148-163, February.
    12. Lihui Tian & Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Pricing Vulnerable Options with Correlated Credit Risk Under Jump‐Diffusion Processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(10), pages 957-979, October.
    13. 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.
    14. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
    15. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    16. Ingolf Dittmann & Ernst Maug & Oliver G. Spalt, 2013. "Indexing Executive Compensation Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 26(12), pages 3182-3224.
    17. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    18. Charles Levi, & Partrat, Christian, 1991. "Statistical Analysis of Natural Events in the United States," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 253-276, November.
    19. Fard, Farzad Alavi, 2015. "Analytical pricing of vulnerable options under a generalized jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 19-28.
    20. 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.
    21. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    22. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    23. 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.
    24. 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.
    25. 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.
    26. Weidong Xu & Weijun Xu & Weilin Xiao, 2015. "Pricing black-scholes options with correlated credit risk and jump risk," Applied Economics Letters, Taylor & Francis Journals, vol. 22(2), pages 87-93, January.
    27. Zhiwei Su & Xingchun Wang, 2019. "Pricing executive stock options with averaging features under the Heston–Nandi GARCH model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(9), pages 1056-1084, 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. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

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    More about this item

    Keywords

    Catastrophe equity put options; Catastrophe risk management; Catastrophic events; Poisson processes; G13;
    All these keywords.

    JEL classification:

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

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