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Large Deviations In Multifactor Portfolio Credit Risk

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  • Paul Glasserman
  • Wanmo Kang
  • Perwez Shahabuddin

Abstract

The measurement of portfolio credit risk focuses on rare but significant large‐loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero. Both limits are also based on letting the size of the portfolio increase. Our analysis reveals a qualitative distinction between the two cases: in the rare‐default regime, the tail of the loss distribution decreases exponentially, but in the large‐threshold regime the decay is consistent with a power law. This indicates that the dependence between defaults imposed by the Gaussian copula is qualitatively different for portfolios of high‐quality and lower‐quality credits.

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  • 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.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:3:p:345-379
    DOI: 10.1111/j.1467-9965.2006.00307.x
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    References listed on IDEAS

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    1. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701.
    2. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190.
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    Cited by:

    1. 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.
    2. 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).
    3. Massimo Morini & Damiano Brigo, 2008. "Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis," Papers 0812.4156, arXiv.org.
    4. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    5. Cheng-Der Fuh & Chuan-Ju Wang, 2017. "Efficient Exponential Tilting for Portfolio Credit Risk," Papers 1711.03744, arXiv.org, revised Apr 2019.
    6. Anand Deo & Sandeep Juneja, 2021. "Credit Risk: Simple Closed-Form Approximate Maximum Likelihood Estimator," Operations Research, INFORMS, vol. 69(2), pages 361-379, March.
    7. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
    8. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    9. 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.
    10. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Portfolio risk analysis of excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 91-110.
    11. Tim J. Brereton & Dirk P. Kroese & Joshua C. Chan, 2012. "Monte Carlo Methods for Portfolio Credit Risk," ANU Working Papers in Economics and Econometrics 2012-579, Australian National University, College of Business and Economics, School of Economics.
    12. Karolina Bujok & Ben Hambly & Christoph Reisinger, 2012. "Multilevel simulation of functionals of Bernoulli random variables with application to basket credit derivatives," Papers 1211.0707, arXiv.org, revised Feb 2018.
    13. Collins, Sean & Gallagher, Emily, 2016. "Assessing the credit risk of money market funds during the eurozone crisis," Journal of Financial Stability, Elsevier, vol. 25(C), pages 150-165.
    14. Konstantinos Spiliopoulos & Richard B. Sowers, 2013. "Default Clustering in Large Pools: Large Deviations," Papers 1311.0498, arXiv.org, revised Feb 2015.
    15. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    16. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2008. "Fast Simulation of Multifactor Portfolio Credit Risk," Operations Research, INFORMS, vol. 56(5), pages 1200-1217, October.
    17. 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.
    18. 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.
    19. 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.
    20. Anand Deo & Sandeep Juneja, 2019. "Credit Risk: Simple Closed Form Approximate Maximum Likelihood Estimator," Papers 1912.12611, arXiv.org.
    21. Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.
    22. Amogh Deshpande, 2014. "Comparing the Value at Risk Performance of the CreditRisk + and its Enhancement: A Large Deviations Approach," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 1009-1023, December.

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