IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/128366.html
   My bibliography  Save this paper

On the last zero process with an application in corporate bankruptcy

Author

Listed:
  • Baurdoux, Erik J.
  • Pedraza, José M.

Abstract

For a spectrally negative L´evy process X, consider gt, the last time X is below the level zero before time t ≥ 0. We use a perturbation method for L´evy processes to derive an Itˆo formula for the threedimensional process {(gt, t,Xt), t ≥ 0} and its infinitesimal generator. Moreover, with Ut := t − gt, the length of a current positive excursion, we derive a general formula that allows us to calculate a functional of the whole path of (U,X) = {(Ut,Xt), t ≥ 0} in terms of the positive and negative excursions of the process X. As a corollary, we find the joint Laplace transform of (Ueq ,Xeq ), where eq is an independent exponential time, and the q-potential measure of the process (U,X). Furthermore, using the results mentioned above, we find a solution to a general optimal stopping problem depending on (U,X) with an application in corporate bankruptcy. Lastly, we establish a link between the optimal prediction of g∞ and optimal stopping problems in terms of (U,X) as per Baurdoux and Pedraza (2024).

Suggested Citation

  • Baurdoux, Erik J. & Pedraza, José M., 2025. "On the last zero process with an application in corporate bankruptcy," LSE Research Online Documents on Economics 128366, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:128366
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/128366/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    2. John K.-H. Quah & Bruno Strulovici, 2013. "Discounting, Values, and Decisions," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 896-939.
    3. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    4. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    5. Damien Lamberton & Mohammed Mikou, 2008. "The critical price for the American put in an exponential Lévy model," Finance and Stochastics, Springer, vol. 12(4), pages 561-581, October.
    6. 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.
    7. Kristoffer Glover & Hardy Hulley, 2014. "Optimal prediction of the last-passage time of a transient diffusion," Published Paper Series 2014-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    8. Gustavo Manso & Bruno Strulovici & Alexei Tchistyi, 2010. "Performance-Sensitive Debt," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 1819-1854.
    9. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    2. Barrieu, Pauline & Bellamy, N., 2007. "Optimal hitting time and perpetual option in a non-Lévy model: application to real options," LSE Research Online Documents on Economics 5099, London School of Economics and Political Science, LSE Library.
    3. Damien Lamberton & Mohammed Mikou, 2013. "Exercise boundary of the American put near maturity in an exponential Lévy model," Finance and Stochastics, Springer, vol. 17(2), pages 355-394, April.
    4. Chi, Yichun, 2010. "Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 385-396, April.
    5. Lando, David & Mortensen, Allan, 2004. "On the Pricing of Step-Up Bonds in the European Telecom Sector," Working Papers 2004-9, Copenhagen Business School, Department of Finance.
    6. Manso, Gustavo, 2013. "Feedback effects of credit ratings," Journal of Financial Economics, Elsevier, vol. 109(2), pages 535-548.
    7. Liu, Bo & Xia, Xin & Yang, Jinqiang, 2017. "Financing constraints and the use of performance-sensitive debt," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 73-84.
    8. 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.
    9. Baurdoux, Erik J. & Pedraza, José M., 2023. "Predicting the last zero before an exponential time of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119290, London School of Economics and Political Science, LSE Library.
    10. Dwight Jaffee & Alexei Tchistyi & Boris Albul, 2013. "Contingent Convertible Bonds and Capital Structure Decisions," 2013 Meeting Papers 682, Society for Economic Dynamics.
    11. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
    12. Shi, Zhan, 2019. "Time-varying ambiguity, credit spreads, and the levered equity premium," Journal of Financial Economics, Elsevier, vol. 134(3), pages 617-646.
    13. Pierre, Erwan & Villeneuve, Stéphane & Warin, Xavier, 2014. "Capital Investment and Liquidity Management with collateralized debt," IDEI Working Papers 841, Institut d'Économie Industrielle (IDEI), Toulouse.
    14. Koziol, Christian & Lawrenz, Jochen, 2010. "Optimal design of rating-trigger step-up bonds: Agency conflicts versus asymmetric information," Journal of Corporate Finance, Elsevier, vol. 16(2), pages 182-204, April.
    15. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    16. Erwan Pierre & St'ephane Villeneuve & Xavier Warin, 2014. "Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line," Papers 1411.7670, arXiv.org, revised Nov 2015.
    17. John Quah & Bruno Strulovici, 2011. "Discounting, Patience, and Dynamic Decision Making," Economics Series Working Papers 555, University of Oxford, Department of Economics.
    18. John K. -H Quah & Bruno Strulovici, 2009. "Discounting and Patience in Optimal Stopping and Control Problems," Discussion Papers 1480, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Martellini, Lionel & Milhau, Vincent & Tarelli, Andrea, 2018. "Capital structure decisions and the optimal design of corporate market debt prograams," Journal of Corporate Finance, Elsevier, vol. 49(C), pages 141-167.
    20. Miao, Zixia & Huang, Yiping & Lv, Yingyi, 2025. "Corporate short-termism and the use of performance-sensitive debt," Finance Research Letters, Elsevier, vol. 75(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:128366. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.