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NUMERICAL PRICING OF CoCo BONDS WITH PARISIAN TRIGGER FEATURE USING THE FORTET METHOD

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  • CHI MAN LEUNG

    (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, P. R. China)

  • YUE KUEN KWOK

    (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, P. R. China)

Abstract

Unlike conventional convertible bonds, contingent convertible (CoCo) bonds are converted into equity shares of the issuing bank subject to certain trigger mechanisms (accounting and/or regulatory trigger) when the issuing bank is under financial nonviable state. We consider pricing of these CoCo bonds using the contingent claims approach, where the state variables are the stock price and Tier 1 capital ratio. We use the Parisian feature to model the regulatory trigger where equity conversion is triggered when the capital ratio stays under the nonviable state consecutively for a certain period of time. The accounting trigger is modeled using the one-touch barrier feature associated with the capital ratio. The Parisian trigger feature adds one extra path dependent state variable in the pricing model of a CoCo bond. We design effective numerical algorithms for pricing the CoCo bonds using the extended Fortet method that avoid adding one extra state variable for the Parisian feature of regulatory trigger. Pricing properties of the CoCo bonds under both regulatory trigger and accounting trigger are explored.

Suggested Citation

  • Chi Man Leung & Yue Kuen Kwok, 2017. "NUMERICAL PRICING OF CoCo BONDS WITH PARISIAN TRIGGER FEATURE USING THE FORTET METHOD," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-22, November.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500467
    DOI: 10.1142/S0219024917500467
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    References listed on IDEAS

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    1. Damiano Brigo & João Garcia & Nicola Pede, 2015. "Coco Bonds Pricing With Credit And Equity Calibrated First-Passage Firm Value Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    2. Stefan Avdjiev & Anastasia Kartasheva & Bilyana Bogdanova, 2013. "CoCos: a primer," BIS Quarterly Review, Bank for International Settlements, September.
    3. Carole Bernard & Olivier Le Courtois & François Quittard-Pinon, 2006. "Development and Pricing of a New Participating Contract," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 179-195.
    4. Tsz-Kin Chung & Yue-Kuen Kwok, 2016. "Enhanced equity-credit modelling for contingent convertibles," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1511-1527, October.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    6. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    7. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 499-516, June.
    8. Pierre Collin‐Dufresne & Robert S. Goldstein, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    9. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, vol. 12(2), pages 195-218, April.
    10. Jan De Spiegeleer & Stephan Höcht & Ine Marquet & Wim Schoutens, 2017. "CoCo bonds and implied CET1 volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 813-824, June.
    11. Paul Glasserman & Behzad Nouri, 2012. "Contingent Capital with a Capital-Ratio Trigger," Management Science, INFORMS, vol. 58(10), pages 1816-1833, October.
    12. Makarov, R. & Metzler, A. & Ni, Z., 2015. "Modelling default risk with occupation times," Finance Research Letters, Elsevier, vol. 13(C), pages 54-65.
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