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Modeling liquidation risk with occupation times

Author

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  • Roman N. Makarov

    (Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada)

Abstract

In this paper, we develop a new structural model that allows for a distinction between default and liquidation to be made. Default occurs when firm’s asset value process crosses a bankruptcy barrier. Here, we do not assume that default immediately triggers liquidation. Instead, the firm is allowed to continue operating even if it is in default. Liquidation is triggered as soon as the firm’s asset value has cumulatively spent a prespecified amount of time below the default barrier or has dropped below the liquidation barrier. The proposed model includes the Black–Cox model as a limiting case. A semi-analytical formula of the liquidation probability is derived for the case where firm’s asset value follows a geometric Brownian motion. Nonlinear volatility diffusion models are discussed as well.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:04:n:s2424786316500286
    DOI: 10.1142/S2424786316500286
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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. Giuseppe Campolieti & Roman N. Makarov & Karl Wouterloot, 2013. "Pricing Step Options under the CEV and other Solvable Diffusion Models," Papers 1302.3771, arXiv.org.
    3. 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.
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    6. Makarov, R. & Metzler, A. & Ni, Z., 2015. "Modelling default risk with occupation times," Finance Research Letters, Elsevier, vol. 13(C), pages 54-65.
    7. 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.
    8. 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.
    9. Yildirim, Yildiray, 2006. "Modeling default risk: A new structural approach," Finance Research Letters, Elsevier, vol. 3(3), pages 165-172, September.
    10. G. Campolieti & R. Makarov & K. Wouterloot, 2013. "Pricing Step Options Under The Cev And Other Solvable Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-36.
    11. 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.
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    Cited by:

    1. 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.
    2. Nguyen, Duy Phat & Borovkov, Konstantin, 2023. "Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 72-81.
    3. Krzysztof Dȩbicki & Peng Liu & Zbigniew Michna, 2020. "Sojourn Times of Gaussian Processes with Trend," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2119-2166, December.

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