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The Fascination of Probability, Statistics and their Applications pp 447–464Cite as

CoCos with Extension Risk. A Structural Approach

Abstract

In this paper we obtain some formulas for pricing contingent convertibles subject to what we call extension risk, i.e., the possibility that the bond issuer does not buy back the bond at pre-specified call dates. We follow a structural approach and we address the finite and infinite maturity cases.

Keywords

  • Contingent capital
  • Coco bond
  • Extension risk
  • Callable bond

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Notes

  1. 1.

    By a lower Snell envelope of a discrete time \(\mathbb {F}\)-adapted process \(X:=\left( X_{i}\right) _{i=1}^{N}\), we understand the minus Snell envelope of \(-X.\) See, for instance, Sect. 2.2 in [14] for the definition of the Snell envelope of a process and its relationship with the problem of optimal stopping.

References

  1. Basel Committe on Banking Supervision. Basel III: A global regulatory framework for more resilient banks and banking systems. Bank for International Settlements (2010)

    Google Scholar 

  2. Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Brigo, D., Garcia, J., Pede, N.: Coco bonds valuation with equity and credit-calibrated first fassage structural models. Preprint (2013)

    Google Scholar 

  4. Chen, N., Glasserman, P., Nouri, B., Pelger, M.: CoCos, bail-in, and tail risk. OFR Working paper. U.S. Department of the Treasury (2013)

    Google Scholar 

  5. Cheridito, P., Xu, Z.: A reduced form CoCo model with deterministic conversion intensity. Preprint (2013)

    Google Scholar 

  6. Cheridito, P., Xu, Z.: Pricing and hedging CoCos. Preprint (2013)

    Google Scholar 

  7. Commission of Experts.: Final report of the commission of experts for limiting the economic risks posed by large companies. Technical report, Swiss National Bank (2010)

    Google Scholar 

  8. Corcuera, J.M., Fajardo, J., Schoutens, W., Jonsson, H., Spiegeleer, J., Valdivia, A.: Close form pricing formulas for coupon cancellable CoCos. J. Bank. Finance 42, 339–351 (2014)

    CrossRef  Google Scholar 

  9. De Spiegeleer, J., Schoutens, W.: Pricing contingent convertibles: a derivatives approach. J. Deriv. 20(2), 27–36 (2012)

    Google Scholar 

  10. De Spiegeleer, J., Schoutens, W.: Multiple trigger CoCos: contingent debt without death spiral risk. Financ. Markets Inst. Instrum. J. 22(2), 129–141 (2013)

    CrossRef  Google Scholar 

  11. De Spiegeleer, J., Schoutens, W.: Coco bonds with extension risk. Wilmott 71, 78–91 (2014)

    CrossRef  Google Scholar 

  12. De Spiegeleer, J., Van Hulle, C., Schoutens, W.: The Handbook of Hybrid Securities: Convertible Bonds. CoCo Bonds and Bail-In. The Wiley Finance Series (2014)

    Google Scholar 

  13. European Banking Authority.: Buffer convertible capital securities—final termsheet. Technical report (2011)

    Google Scholar 

  14. Lamberton, D., Lapeyre, B.: Introduction to Stochastic Calculus Applied to Finance. Financial Mathematics Series. Chapman & Hall/CRC (2007)

    Google Scholar 

  15. Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modelling. Applications of Mathematics (New York), vol. 36. Springer, Berlin (1997)

    Google Scholar 

  16. Peskir, G., Shiryaev, A.N.: Optimal Stopping and Free-Boundary Problems. Lectures in Mathematics. ETH Zurich. Birkhauser, Basel (2006)

    Google Scholar 

  17. Yu, P., Van Luu, B.: Lessons from the collapse in hybrid bank capital securities. Int. J. Manage. Pract. 5(2), 125–148 (2012)

    CrossRef  Google Scholar 

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Acknowledgments

The work of J.M. Corcuera is supported by the Grant of the Spanish MCINN MTM2013-40782. This research was partially carried out at CAS—Centre for Advanced Study at the Norwegian Academy of Science and Letters, Research group SEFE. J. Fajardo thanks financial support from CNPQ, grant 471131/2013-0.

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Authors and Affiliations

  1. University of Barcelona, Gran Via de Les Corts Catalanes, 585, 08007, Barcelona, Spain

    José Manuel Corcuera & Arturo Valdivia

  2. EBAPE, Getulio Vargas Foundation, Rio de Janeiro, Brazil

    José Fajardo

  3. Catholic University of Leuven, Leuven, Belgium

    Wim Schoutens

Authors
  1. José Manuel Corcuera
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  2. José Fajardo
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  3. Wim Schoutens
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  4. Arturo Valdivia
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Corresponding author

Correspondence to José Manuel Corcuera .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aarhus, Aarhus, Denmark

    Mark Podolskij

  2. Institute of Mathematical Finance, Ulm University, Ulm, Germany

    Robert Stelzer

  3. Department of Mathematics, University of Aarhus, Aarhus C, Denmark

    Steen Thorbjørnsen

  4. Department of Mathematics Huxley Building, Room 551, Imperial College London, London, United Kingdom

    Almut E. D. Veraart

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Corcuera, J.M., Fajardo, J., Schoutens, W., Valdivia, A. (2016). CoCos with Extension Risk. A Structural Approach. In: Podolskij, M., Stelzer, R., Thorbjørnsen, S., Veraart, A. (eds) The Fascination of Probability, Statistics and their Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-25826-3_21

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