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Default probabilities and default correlations under stress

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  • Packham, Natalie
  • Kalkbrener, Michael
  • Overbeck, Ludger

Abstract

We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. The analysis is performed in the class of elliptical distributions, a family of light-tailed to heavy-tailed distributions encompassing many distributions commonly found in financial modelling. It turns out that the asymptotic limit of default probabilities and default correlations depend on the max-domain of the elliptical distribution's mixing variable. In case the mixing variable is regularly varying, default probabilities are strictly smaller than 1 and default correlations are in (0; 1). Both can be expressed in terms of the Student t-distribution function. In the rapidly varying case, default probabilities are 1 and default correlations are 0. We compare our results to the tail dependence function and discuss implications for credit portfolio modelling.

Suggested Citation

  • Packham, Natalie & Kalkbrener, Michael & Overbeck, Ludger, 2014. "Default probabilities and default correlations under stress," Frankfurt School - Working Paper Series 211, Frankfurt School of Finance and Management.
    • Handle: RePEc:zbw:fsfmwp:211
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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. Klaus Duellmann & Martin Erdelmeier, 2009. "Crash Testing German Banks," International Journal of Central Banking, International Journal of Central Banking, vol. 5(3), pages 139-175, September.
    3. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718, December.
    4. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    5. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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    Cited by:

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    2. Cai, Zongwu & Fang, Ying & Lin, Ming & Su, Jia, 2018. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," IRTG 1792 Discussion Papers 2018-047, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
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    4. Yan, Ji Gao, 2018. "Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables," IRTG 1792 Discussion Papers 2018-040, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    7. Xiaojia Bao & Qingliang Fan, 2020. "The impact of temperature on gaming productivity: evidence from online games," Empirical Economics, Springer, vol. 58(2), pages 835-867, February.
    8. Kuczmaszewska, Anna & Yan, Ji Gao, 2018. "On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables," IRTG 1792 Discussion Papers 2018-041, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Nasekin, Sergey & Chen, Cathy Yi-Hsuan, 2018. "Deep learning-based cryptocurrency sentiment construction," IRTG 1792 Discussion Papers 2018-066, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Zbonakova, Lenka & Li, Xinjue & Härdle, Wolfgang Karl, 2018. "Penalized Adaptive Forecasting with Large Information Sets and Structural Changes," IRTG 1792 Discussion Papers 2018-039, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    Keywords

    financial risk management; credit portfolio modelling; stress testing; elliptic distribution; max-domain;
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