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Time reversal and last passage time of diffusions with applications to credit risk management

Author

Listed:
  • Masahiko Egami

    (Kyoto University)

  • Rusudan Kevkhishvili

    (Kyoto University)

Abstract

We study time reversal, last passage time and h $h$ -transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyse the distribution of the time left until killing after the last passage time. With these tools, we develop a new risk management framework for companies based on the leverage process (the ratio of a company asset process over its debt) and its corresponding alarming level. We also suggest how a company can determine the alarming level for the leverage process by constructing a relevant optimisation problem.

Suggested Citation

  • Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:3:d:10.1007_s00780-020-00423-6
    DOI: 10.1007/s00780-020-00423-6
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    References listed on IDEAS

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    1. 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.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    3. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    4. Ross Williams, 2013. "Introduction," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 46(4), pages 460-461, December.
    5. Lehar, Alfred, 2005. "Measuring systemic risk: A risk management approach," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2577-2603, October.
    6. Jin‐Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167, April.
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    Cited by:

    1. Landriault, David & Li, Bin & Lkabous, Mohamed Amine & Wang, Zijia, 2023. "Bridging the first and last passage times for Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 308-334.
    2. Baurdoux, Erik J. & Pedraza, José M., 2024. "Lp optimal prediction of the last zero of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119468, London School of Economics and Political Science, LSE Library.
    3. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Post-Last Exit Time Process and its Application to Loss-Given-Default Distribution," Papers 2009.00868, arXiv.org, revised Mar 2024.

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    More about this item

    Keywords

    Time reversal; Linear diffusion; Last passage time; h $h$ -transform; Risk management;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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