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Asymptotics for credit portfolio losses due to defaults in a multi-sector model

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Listed:
  • Shaoying Chen

    (Nanjing Audit University)

  • Yang Yang

    (Nanjing Audit University)

  • Zhimin Zhang

    (Chongqing University)

Abstract

Consider a credit portfolio with the investments in various sectors and exposed to an external stochastic environment. The portfolio loss due to defaults is of critical importance for social and economic security particularly in times of financial distress. We argue that the dependences among obligors within sectors (intradependence) and across sectors (interdependence) may coexist and influence the portfolio loss. To quantify the portfolio loss, we develop a multi-sector structural model in which a multivariate regular variation structure is employed to model the intradependence within sectors, and the interdependence across sectors is implied in the arbitrarily dependent macroeconomic factors, although, given them, obligors in different sectors are conditionally independent. We establish some sharp asymptotic formulas for the tail probability and the (tail) distortion risk measures of the portfolio loss. Our results show that the portfolio loss is mainly driven by the latent variables and the recovery rate function, and is also potentially affected by the macroeconomic factors and the intradependence within sectors. Moreover, we implement intensive numerical studies to examine the accuracy of the obtained approximations and conduct some sensitivity analysis.

Suggested Citation

  • Shaoying Chen & Yang Yang & Zhimin Zhang, 2024. "Asymptotics for credit portfolio losses due to defaults in a multi-sector model," Annals of Operations Research, Springer, vol. 337(1), pages 23-44, June.
    • Handle: RePEc:spr:annopr:v:337:y:2024:i:1:d:10.1007_s10479-024-05934-5
    DOI: 10.1007/s10479-024-05934-5
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    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Yi He & John H. J. Einmahl, 2017. "Estimation of extreme depth-based quantile regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 449-461, March.
    3. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    4. Zhou, Chen, 2010. "Dependence structure of risk factors and diversification effects," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 531-540, June.
    5. Tabak, Benjamin M. & Fazio, Dimas M. & Cajueiro, Daniel O., 2011. "The effects of loan portfolio concentration on Brazilian banks' return and risk," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3065-3076, November.
    6. John H. J. Einmahl & Fan Yang & Chen Zhou, 2021. "Testing the Multivariate Regular Variation Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 907-919, October.
    7. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    8. Serguei Foss & Andrew Richards, 2010. "On Sums of Conditionally Independent Subexponential Random Variables," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 102-119, February.
    9. Chen, Peimin & Wu, Chunchi, 2014. "Default prediction with dynamic sectoral and macroeconomic frailties," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 211-226.
    10. Zhu, Li & Li, Haijun, 2012. "Tail distortion risk and its asymptotic analysis," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 115-121.
    11. Chitru S. Fernando & Anthony D. May & William L. Megginson, 2012. "The Value of Investment Banking Relationships: Evidence from the Collapse of Lehman Brothers," Journal of Finance, American Finance Association, vol. 67(1), pages 235-270, February.
    12. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    13. Mainik, Georg & Embrechts, Paul, 2013. "Diversification in heavy-tailed portfolios: properties and pitfalls," Annals of Actuarial Science, Cambridge University Press, vol. 7(1), pages 26-45, March.
    14. Gabriel Hawawini & Venkat Subramanian & Paul Verdin, 2003. "Is performance driven by industry‐or firm‐specific factors? A new look at the evidence," Strategic Management Journal, Wiley Blackwell, vol. 24(1), pages 1-16, January.
    15. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    16. Barbe, Philippe & Fougères, Anne-Laure & Genest, Christian, 2006. "On the Tail Behavior of Sums of Dependent Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 361-373, November.
    17. Calabrese, Raffaella, 2023. "Contagion effects of UK small business failures: A spatial hierarchical autoregressive model for binary data," European Journal of Operational Research, Elsevier, vol. 305(2), pages 989-997.
    18. H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
    19. Pais, Amelia & Stork, Philip A., 2011. "Contagion risk in the Australian banking and property sectors," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 681-697, March.
    20. Cai, J. & Einmahl, J.H.J. & de Haan, L.F.M., 2011. "Estimation of extreme risk regions under multivariate regular variation," Other publications TiSEM b7a72a8d-f9bc-4129-ae9b-a, Tilburg University, School of Economics and Management.
    21. Liu, Jing, 2018. "LLN-type approximations for large portfolio losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 71-77.
    22. Glasserman, Paul & Young, H. Peyton, 2016. "Contagion in financial networks," LSE Research Online Documents on Economics 68681, London School of Economics and Political Science, LSE Library.
    23. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    24. Qihe Tang & Zhongyi Yuan, 2013. "Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(3), pages 253-271.
    25. Jorion, Philippe & Zhang, Gaiyan, 2007. "Good and bad credit contagion: Evidence from credit default swaps," Journal of Financial Economics, Elsevier, vol. 84(3), pages 860-883, June.
    26. Fan Yang, 2015. "First- and Second-order Asymptotics for the Tail Distortion Risk Measure of Extreme Risks," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 520-532, February.
    27. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    28. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Other publications TiSEM 261583f5-c571-48c6-8cea-9, Tilburg University, School of Economics and Management.
    29. de Haan, L. & Resnick, S. I., 1981. "On the observation closest to the origin," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 301-308, August.
    30. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Discussion Paper 2023-001, Tilburg University, Center for Economic Research.
    31. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    32. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2015. "Large Portfolio Asymptotics For Loss From Default," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 77-114, January.
    33. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    34. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    35. Xi-Ren Cao & Xiangwei Wan, 2017. "Sensitivity Analysis Of Nonlinear Behavior With Distorted Probability," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 115-150, January.
    36. Qihe Tang & Yang Yang, 2019. "Interplay of insurance and financial risks in a stochastic environment," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(5), pages 432-451, May.
    37. Howard Qi & Jian Shi & Yan Alice Xie, 2019. "Default correlation: rating, industry ripple effect, and business cycle," Applied Economics, Taylor & Francis Journals, vol. 51(30), pages 3256-3273, June.
    38. Francis A. Longstaff & Arvind Rajan, 2008. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 63(2), pages 529-563, April.
    39. 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.
    40. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    41. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.
    42. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    43. 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.
    44. Paul Glasserman & H. Peyton Young, 2016. "Contagion in Financial Networks," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 779-831, September.
    45. Achal Bassamboo & Sandeep Juneja & Assaf Zeevi, 2008. "Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation," Operations Research, INFORMS, vol. 56(3), pages 593-606, June.
    46. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    47. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
    48. Weng, Chengguo & Zhang, Yi, 2012. "Characterization of multivariate heavy-tailed distribution families via copula," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 178-186.
    49. Shi, Xiaojun & Tang, Qihe & Yuan, Zhongyi, 2017. "A limit distribution of credit portfolio losses with low default probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 156-167.
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    More about this item

    Keywords

    Credit portfolio loss due to defaults; Multi-sector model; Sharp asymptotics; Macroeconomic factors; Multivariate regular variation;
    All these keywords.

    JEL classification:

    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • 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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