IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v88y2019icp238-254.html
   My bibliography  Save this article

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Author

Listed:
  • Burnecki, Krzysztof
  • Giuricich, Mario Nicoló
  • Palmowski, Zbigniew

Abstract

Within the context of banking-related literature on contingent convertible bonds, we comprehensively formalise the design and features of a relatively new type of insurance-linked security, called a contingent convertible catastrophe bond (CocoCat). We begin with a discussion on its design and compare its relative merits to catastrophe bonds and catastrophe-equity puts. Subsequently, we derive analytical valuation formulae for index-linked CocoCats under the assumption of independence between natural catastrophe and financial market risks. We model natural catastrophe losses by a time-inhomogeneous compound Poisson process, with the interest-rate process governed by the Longstaff model. By using an exponential change of measure on the loss process, as well as a Girsanov-like transformation to synthetically remove the correlation between the share and interest-rate processes, we obtain these analytical formulae. Using selected parameter values in line with earlier research, we numerically analyse our valuation formulae for index-linked CocoCats. An analysis of the results reveals that the CocoCat prices are most sensitive to changing interest-rates, conversion fractions and the threshold levels defining the trigger times.

Suggested Citation

  • Burnecki, Krzysztof & Giuricich, Mario Nicoló & Palmowski, Zbigniew, 2019. "Valuation of contingent convertible catastrophe bonds — The case for equity conversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 238-254.
  • Handle: RePEc:eee:insuma:v:88:y:2019:i:c:p:238-254
    DOI: 10.1016/j.insmatheco.2019.07.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668718301598
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2019.07.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.
    2. Mark J. Flannery, 2016. "Stabilizing Large Financial Institutions with Contingent Capital Certificates," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-26, June.
    3. 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.
    4. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    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. Delbaen, F. & Haezendonck, J., 1989. "A martingale approach to premium calculation principles in an arbitrage free market," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 269-277, December.
    9. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    12. Beaglehole, David & Tenney, Mark, 1992. "Corrections and additions to 'a nonlinear equilibrium model of the term structure of interest rates'," Journal of Financial Economics, Elsevier, vol. 32(3), pages 345-353, December.
    13. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    14. Bjoern Hagendorff & Jens Hagendorff & Kevin Keasey, 2015. "The Impact of Mega‐Catastrophes on Insurers: An Exposure‐Based Analysis of the U.S. Homeowners’ Insurance Market," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 157-173, January.
    15. 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.
    16. 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.
    17. Duan, Jin-Chuan & Simonato, Jean-Guy, 2002. "Maximum likelihood estimation of deposit insurance value with interest rate risk," Journal of Empirical Finance, Elsevier, vol. 9(1), pages 109-132, January.
    18. 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.
    19. Alexander Braun, 2016. "Pricing in the Primary Market for Cat Bonds: New Empirical Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 811-847, December.
    20. Chi-Fai Lo & Cho-Hoi Hui, 2016. "Pricing corporate bonds with interest rates following double square-root process," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-31, September.
    21. Jean-Luc Besson & Michel M Dacorogna & Paolo de Martin & Michael Kastenholz & Michael Moller, 2009. "How Much Capital Does a Reinsurance Need?," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 34(2), pages 159-174, April.
    22. Samuel Cox & Hal Pedersen, 2000. "Catastrophe Risk Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 56-82.
    23. David Durbin, 2001. "Managing Natural Catastrophe Risks: The Structure and Dynamics of Reinsurance*," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 26(2), pages 297-309, April.
    24. Haslip, Gareth G. & Kaishev, Vladimir K., 2010. "Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 307-329, May.
    25. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    26. Kemp, M.H.D., 1997. "Actuaries and Derivatives," British Actuarial Journal, Cambridge University Press, vol. 3(1), pages 51-180, April.
    27. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545, September.
    28. Andreas Müller & Marcel Grandi, 2000. "Weather Derivatives: A Risk Management Tool for Weather-sensitive Industries," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 25(2), pages 273-287, April.
    29. 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.
    30. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    31. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    32. 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.
    33. Chi-Fai Lo & Cho-Hoi Hui, 2016. "Pricing Corporate Bonds With Interest Rates Following Double Square-root Process," Working Papers 112016, Hong Kong Institute for Monetary Research.
    34. 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.
    35. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    36. Vaugirard, Victor E., 2003. "Pricing catastrophe bonds by an arbitrage approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(1), pages 119-132.
    37. Marc Gürtler & Martin Hibbeln & Christine Winkelvos, 2016. "The Impact of the Financial Crisis and Natural Catastrophes on CAT Bonds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 579-612, September.
    38. Robert E. Hoyt & Kathleen A. McCullough, 1999. "Catastrophe Insurance Options: Are They Zero-Beta Assets?," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 147-163.
    39. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    40. Giuseppe De Martino & Massimo Libertucci & Mario Marangoni & Mario Quagliariello, 2010. "Countercyclical contingent capital (CCC): possible use and ideal design," Questioni di Economia e Finanza (Occasional Papers) 71, Bank of Italy, Economic Research and International Relations Area.
    41. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    42. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    43. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    44. Peter Carayannopoulos & M Fabricio Perez, 2015. "Diversification through Catastrophe Bonds: Lessons from the Subprime Financial Crisis," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(1), pages 1-28, January.
    45. Carolyn W. Chang & Jack S. K. Chang, 2017. "An Integrated Approach to Pricing Catastrophe Reinsurance," Risks, MDPI, vol. 5(3), pages 1-12, September.
    46. Milidonis, Andreas & Grace, Martin F., 2008. "Tax-Deductible Pre-Event Catastrophe Loss Reserves: The Case of Florida1," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 13-51, May.
    47. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    48. 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.
    49. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    50. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Massimo Arnone & Michele Leonardo Bianchi & Anna Grazia Quaranta & Gian Luca Tassinari, 2021. "Catastrophic risks and the pricing of catastrophe equity put options," Computational Management Science, Springer, vol. 18(2), pages 213-237, June.
    2. Philippe Oster, 2020. "Contingent Convertible bond literature review: making everything and nothing possible?," Journal of Banking Regulation, Palgrave Macmillan, vol. 21(4), pages 343-381, December.
    3. Wu, Yang-Che, 2020. "Equilibrium in natural catastrophe insurance market under disaster-resistant technologies, financial innovations and government interventions," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 116-128.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Research Paper Series 379, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    3. Ben Ammar, Semir & Braun, Alexander & Eling, Martin, 2015. "Alternative Risk Transfer and Insurance-Linked Securities: Trends, Challenges and New Market Opportunities," I.VW HSG Schriftenreihe, University of St.Gallen, Institute of Insurance Economics (I.VW-HSG), volume 56, number 56.
    4. 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).
    5. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    6. Carolyn W. Chang & Jack S. K. Chang & Min‐Teh Yu & Yang Zhao, 2020. "Portfolio optimization in the catastrophe space," European Financial Management, European Financial Management Association, vol. 26(5), pages 1414-1448, November.
    7. Shao, Jia & Papaioannou, Apostolos D. & Pantelous, Athanasios A., 2017. "Pricing and simulating catastrophe risk bonds in a Markov-dependent environment," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 68-84.
    8. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    9. Krzysztof Burnecki & Mario Nicoló Giuricich, 2017. "Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing," Risks, MDPI, vol. 5(4), pages 1-19, December.
    10. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    11. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    12. Dixon Domfeh & Arpita Chatterjee & Matthew Dixon, 2022. "A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives," Papers 2205.04520, arXiv.org.
    13. Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    14. Sukono & Hafizan Juahir & Riza Andrian Ibrahim & Moch Panji Agung Saputra & Yuyun Hidayat & Igif Gimin Prihanto, 2022. "Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    15. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
    16. Peter Carayannopoulos & Olga Kanj & M. Fabricio Perez, 2022. "Pricing dynamics in the market for catastrophe bonds," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 172-202, January.
    17. 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.
    18. Hui, Cho-Hoi & Lo, Chi-Fai & Chau, Po-Hon, 2018. "Exchange rate dynamics and US dollar-denominated sovereign bond prices in emerging markets," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 109-128.
    19. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).
    20. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:88:y:2019:i:c:p:238-254. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.