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The valuation of contingent capital with catastrophe risks

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Author Info

  • 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.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 45 (2009)
Issue (Month): 1 (August)
Pages: 65-73

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Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:65-73

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Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Doubly stochastic Poisson process Catastrophe risks Contingent capital;

References

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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, Massachusetts Institute of Technology (MIT), Sloan School of Management 1523-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  2. Myers, Stewart C, 1984. " The Capital Structure Puzzle," Journal of Finance, American Finance Association, American Finance Association, vol. 39(3), pages 575-92, July.
  3. 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, Western Risk and Insurance Association, vol. 22(2), pages 125-146.
  4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. Stewart C. Myers, 1984. "Capital Structure Puzzle," NBER Working Papers 1393, National Bureau of Economic Research, Inc.
  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  7. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(3), pages 383-410.
  8. Krzysztof Burnecki & Grzegorz Kukla & Rafal Weron, 2000. "Property insurance loss distributions," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/00/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  9. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 211-239.
  10. Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(3), pages 469-483, June.
  11. Leland, Hayne E & Pyle, David H, 1977. "Informational Asymmetries, Financial Structure, and Financial Intermediation," Journal of Finance, American Finance Association, American Finance Association, vol. 32(2), pages 371-87, May.
  12. 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, Elsevier, vol. 13(2), pages 187-221, June.
  13. repec:fth:geneec:99.01 is not listed on IDEAS
  14. 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.
  15. Myers, Stewart C., 1984. "Capital structure puzzle," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 1548-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  16. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2004. "Valuation of structured risk management products," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 34(2), pages 259-272, April.
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Cited by:
  1. 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, Elsevier, vol. 37(12), pages 5025-5035.
  2. Gunther Leobacher & Philip Ngare, 2014. "Utility indifference pricing of derivatives written on industrial loss indexes," Papers, arXiv.org 1404.0879, arXiv.org.

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