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Modelling default risk with occupation times

Author

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  • Makarov, R.
  • Metzler, A.
  • Ni, Z.

Abstract

This paper develops a semi-analytic pricing formula, easily implemented via quadrature, for a structural model based on occupation times that contains both the Merton and Black–Cox models as limiting cases. In the model liquidation is triggered as soon as the firm’s asset value has spent a prespecified amount of time below the default barrier. Surprisingly, we find that the value of the firm’s debt (i) need not be monotone in the length of the grace period and (ii) need not lie between the limiting Merton and Black–Cox values.

Suggested Citation

  • Makarov, R. & Metzler, A. & Ni, Z., 2015. "Modelling default risk with occupation times," Finance Research Letters, Elsevier, vol. 13(C), pages 54-65.
    • Handle: RePEc:eee:finlet:v:13:y:2015:i:c:p:54-65
    DOI: 10.1016/j.frl.2015.03.003
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    References listed on IDEAS

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    1. Franck Moraux, 2002. "Valuing corporate liabilities when the default threshold is not an absorbing barrier," Post-Print halshs-00077168, HAL.
    2. Galai, Dan & Raviv, Alon & Wiener, Zvi, 2007. "Liquidation triggers and the valuation of equity and debt," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3604-3620, December.
    3. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    4. Yildirim, Yildiray, 2006. "Modeling default risk: A new structural approach," Finance Research Letters, Elsevier, vol. 3(3), pages 165-172, September.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. Mark Broadie & Mikhail Chernov & Suresh Sundaresan, 2007. "Optimal Debt and Equity Values in the Presence of Chapter 7 and Chapter 11," Journal of Finance, American Finance Association, vol. 62(3), pages 1341-1377, June.
    7. Hooghiemstra, Gerard, 2002. "On explicit occupation time distributions for Brownian processes," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 405-417, February.
    8. Bin Li & Qihe Tang & Lihe Wang & Xiaowen Zhou, 2014. "Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-19.
    9. Broadie, Mark & Kaya, Özgür, 2007. "A Binomial Lattice Method for Pricing Corporate Debt and Modeling Chapter 11 Proceedings," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(2), pages 279-312, June.
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    Citations

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    Cited by:

    1. Roman N. Makarov, 2016. "Modeling liquidation risk with occupation times," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-11, December.
    2. Giuseppe Campolieti & Hiromichi Kato & Roman N. Makarov, 2022. "Spectral Expansions for Credit Risk Modelling with Occupation Times," Risks, MDPI, vol. 10(12), pages 1-20, November.
    3. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    4. Etienne Chevalier & Vathana Ly Vath & Alexandre Roch, 2020. "Optimal Dividend and Capital Structure with Debt Covenants," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 535-565, November.
    5. 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.

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    More about this item

    Keywords

    Occupation time; Credit risk; Merton model; Black–Cox model; Structural models;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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