IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2011y2011i1n354171.html

Sample‐Path Large Deviations in Credit Risk

Author

Listed:
  • V. J. G. Leijdekker
  • M. R. H. Mandjes
  • P. J. C. Spreij

Abstract

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample‐path large deviation principle (LDP) for the portfolio′s loss process, which enables the computation of the logarithmic decay rate of the probabilities of interest. In addition, we derive exact asymptotic results for a number of specific rare‐event probabilities, such as the probability of the loss process exceeding some given function.

Suggested Citation

  • V. J. G. Leijdekker & M. R. H. Mandjes & P. J. C. Spreij, 2011. "Sample‐Path Large Deviations in Credit Risk," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:354171
    DOI: 10.1155/2011/354171
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2011/354171
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/354171?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Peter Kall, 1986. "Approximation to Optimization Problems: An Elementary Review," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 9-18, February.
    2. Gordy, Michael B., 2002. "Saddlepoint approximation of CreditRisk+," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1335-1353, July.
    3. Lucas, Andre & Klaassens, Pieter & Spreij, Peter & Straetmans, Stefan, 2002. "Erratum to "An analytic approach to credit risk of large corporate bond and loan portfolios" [Journal of Banking and Finance 25, no. 9, pp. 1635-1664]," Journal of Banking & Finance, Elsevier, vol. 26(1), pages 201-202, January.
    4. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2007. "Large Deviations In Multifactor Portfolio Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 345-379, July.
    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. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 237-280, Spring.
    2. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    3. Spiliopoulos, Konstantinos & Sowers, Richard B., 2011. "Recovery rates in investment-grade pools of credit assets: A large deviations analysis," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2861-2898.
    4. Mohamed A. Ayadi & Hatem Ben-Ameur & Nabil Channouf & Quang Khoi Tran, 2019. "NORTA for portfolio credit risk," Annals of Operations Research, Springer, vol. 281(1), pages 99-119, October.
    5. Tang, Qihe & Tang, Zhaofeng & Yang, Yang, 2019. "Sharp asymptotics for large portfolio losses under extreme risks," European Journal of Operational Research, Elsevier, vol. 276(2), pages 710-722.
    6. Hsieh, Ming-Hua & Lee, Yi-Hsi & Shyu, So-De & Chiu, Yu-Fen, 2019. "Estimating multifactor portfolio credit risk: A variance reduction approach," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    7. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    8. Tang, Qihe & Tong, Zhiwei & Yang, Yang, 2021. "Large portfolio losses in a turbulent market," European Journal of Operational Research, Elsevier, vol. 292(2), pages 755-769.
    9. Barro, Diana & Basso, Antonella, 2010. "Credit contagion in a network of firms with spatial interaction," European Journal of Operational Research, Elsevier, vol. 205(2), pages 459-468, September.
    10. Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    11. K. Bujok & B. M. Hambly & C. Reisinger, 2015. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 579-604, September.
    12. Anand Deo & Sandeep Juneja, 2021. "Credit Risk: Simple Closed-Form Approximate Maximum Likelihood Estimator," Operations Research, INFORMS, vol. 69(2), pages 361-379, March.
    13. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, October.
    14. Gagliardini, P. & Gourieroux, C., 2005. "Migration correlation: Definition and efficient estimation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 865-894, April.
    15. André Lucas & Siem Jan Koopman, 2005. "Business and default cycles for credit risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 311-323.
    16. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    17. Gunter Loffler, 2004. "Implied asset value distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 14(12), pages 875-883.
    18. Mathias Lé & Sandrine Lecarpentier & Henri Fraisse & Michel Dietsch, 2019. "Lower bank capital requirements as a policy tool to support credit to SMEs: evidence from a policy experiment," Working Papers hal-04141885, HAL.
    19. Petr Jakubik, 2008. "Credit risk and stress testing of the Czech Banking Sector," ACTA VSFS, University of Finance and Administration, vol. 2(1), pages 107-123.
    20. A. Karas & K. Schoors & G. Lanine, 2008. "Liquidity matters: Evidence from the Russian interbank market," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/520, Ghent University, Faculty of Economics and Business Administration.

    More about this item

    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:wly:jnljam:v:2011:y:2011:i:1:n:354171. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.