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The valuation of contingent capital with catastrophe risks

Author

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  • Lin, Shih-Kuei
  • Chang, Chia-Chien
  • Powers, Michael R.

Abstract

The Intergovernmental Panel on Climate Change Fourth Assessment Report (2007) indicates that unanticipated catastrophic events could increase with time because of global warming. Therefore, it seems inadequate to assume that arrival process of catastrophic events follows a pure Poisson process adopted by most previous studies (e.g. [Louberge, H., Kellezi, E., Gilli, M., 1999. Using catastrophe-linked securities to diversify insurance risk: A financial analysis of lCAT bonds. J. Risk Insurance 22, 125-146; Lee, J.-P., Yu, M.-T., 2002. Pricing default-risky CAT bonds with moral hazard and basis risk. J. Risk Insurance 69, 25-44; Cox, H., Fairchild, J., Pedersen, H., 2004. Valuation of structured risk management products. Insurance Math. Econom. 34, 259-272; Jaimungal, S., Wang, T., 2006. Catastrophe options with stochastic interest rates and compound Poisson losses. Insurance Math. Econom., 38, 469-483]. In order to overcome this shortcoming, this paper proposes a doubly stochastic Poisson process to model the arrival process for catastrophic events. Furthermore, we generalize the assumption in the last reference mentioned above to define the general loss function presenting that different specific loss would have different impacts on the drop in stock price. Based on modeling the arrival rates for catastrophe risks, the pricing formulas of contingent capital are derived by the Merton measure. Results of empirical experiments of contingent capital prices as well as sensitivity analyses are presented.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:65-73
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    References listed on IDEAS

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    1. Myers, Stewart C. & Majluf, Nicolás S., 1945-, 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Working papers 1523-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Stewart C. Myers & Nicholas S. Majluf, 1984. "Corporate Financing and Investment Decisions When Firms Have InformationThat Investors Do Not Have," NBER Working Papers 1396, National Bureau of Economic Research, Inc.
    3. Myers, Stewart C. & Majluf, Nicholas S., 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Journal of Financial Economics, Elsevier, vol. 13(2), pages 187-221, June.
    4. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
    5. 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.
    6. Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
    7. David Cummins & Christopher Lewis & Richard Phillips, 1999. "Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss," NBER Chapters,in: The Financing of Catastrophe Risk, pages 93-148 National Bureau of Economic Research, Inc.
    8. Leland, Hayne E & Pyle, David H, 1977. "Informational Asymmetries, Financial Structure, and Financial Intermediation," Journal of Finance, American Finance Association, vol. 32(2), pages 371-387, May.
    9. repec:fth:geneec:99.01 is not listed on IDEAS
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. Myers, Stewart C., 1984. "Capital structure puzzle," Working papers 1548-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. Myers, Stewart C, 1984. " The Capital Structure Puzzle," Journal of Finance, American Finance Association, vol. 39(3), pages 575-592, July.
    13. 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.
    14. Stewart C. Myers, 1984. "Capital Structure Puzzle," NBER Working Papers 1393, National Bureau of Economic Research, Inc.
    15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    16. Henri Louberge & Evis Kellezi & Manfred Gilli, 1999. "Using Catastrophe-Linked Securities to Diversity Insurance Risk: A Financial Analysis of Cat Bonds," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 125-146.
    17. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
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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. Wu, Yang-Che, 2015. "Reexamining the feasibility of diversification and transfer instruments on smoothing catastrophe risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 54-66.
    3. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    4. Kim, Hwa-Sung & Kim, Bara & Kim, Jerim, 2014. "Pricing perpetual American CatEPut options when stock prices are correlated with catastrophe losses," Economic Modelling, Elsevier, vol. 41(C), pages 15-22.
    5. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
    6. Andreas Eichler & Gunther Leobacher & Michaela Szolgyenyi, 2016. "Utility Indifference Pricing of Insurance Catastrophe Derivatives," Papers 1607.01110, arXiv.org, revised May 2017.
    7. 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.
    8. Têtu Alexandre & Lai Van Son & Soumaré Issouf & Gendron Michel, 2015. "Hedging Flood Losses Using Cat Bonds," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(2), pages 149-184, July.
    9. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    10. 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.

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