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The impact of skew on the pricing of CoCo bonds

Author

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  • Jan De Spiegeleer

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium†RiskConcile, Voie du Chariot 3, 1003 Lausanne, Switzerland)

  • Monika B. Forys

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium)

  • Ine Marquet

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium)

  • Wim Schoutens

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium)

Abstract

This paper presents a Heston-based pricing model for contingent convertible bonds (CoCos). The main finding is that skew in the implied volatility surface has a significant impact on the CoCo price. Hence stochastic volatility models, like the Heston model, which incorporate smile and skew are appropriate in the context of pricing CoCos. The financial crisis of 2007–2008 triggered an avalanche of financial worries for financial institutions around the globe. After the collapse of Lehman Brothers, governments intervened and bailed out banks using tax-payer’s money. Preventing such bail-outs in the future and designing a more stable banking sector in general, requires both higher capital levels and regulatory capital of a higher quality. Bank debt needed therefore to be made absorbing. This is where CoCos come in. The Lloyds Banking Group introduced the first CoCo bonds as early as December 2009. Since the first issuance of a CoCo bond more than five years ago, the market has continued to grow and has now reached a size over €120bn. CoCos are hybrid financial instruments that convert into equity or suffer a write-down of the face value upon the appearance of a trigger event, often in terms of the bank’s CET1 level in combination with a regulatory trigger. The valuation of CoCos boils down to the quantification of the trigger probability and the expected loss suffered by the investors if such a trigger event eventually takes place. There are at least two schools of thought regarding valuation of CoCos. Structural models can be put at work or investors can rely on market implied models. The latter category uses market data (share prices, CDS levels and implied volatility, etc.) in order to calculate the theoretical price of a CoCo bond. In De Spiegeleer and Schoutens The Journal of Derivatives, the pricing of CoCo notes has been worked out in a market implied Black–Scholes context. In this paper we move away from the assumption of a constant volatility which is the back-bone of Black–Scholes based valuation and put the Heston model at work and study CoCos in a stochastic volatility context. The existence of a semi closed-form formula for European options pricing under the Heston model allows for a fast calibration of the model. In our approach we combined market quotes of listed option prices with CDS data. As a case study, the procedure was applied on the Tier 2 10NC 758% CoCo issued by Barclays in 2012.

Suggested Citation

  • Jan De Spiegeleer & Monika B. Forys & Ine Marquet & Wim Schoutens, 2017. "The impact of skew on the pricing of CoCo bonds," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-19, March.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500128
    DOI: 10.1142/S2424786317500128
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    References listed on IDEAS

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    1. Pennacchi, George & Vermaelen, Theo & Wolff, Christian C. P., 2014. "Contingent Capital: The Case of COERCs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 541-574, June.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Stan Maes & Wim Schoutens, 2012. "Contingent Capital: An In-Depth Discussion," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 41(1-2), pages 59-79, February.
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    Cited by:

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    2. Mikhail S. Makushkin, 2024. "Yield Factors of Additional Tier 1 Bonds," Finansovyj žhurnal — Financial Journal, Financial Research Institute, Moscow 125375, Russia, issue 5, pages 43-59, October.
    3. 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.

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