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Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models

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  • Yang, Bill Huajian

Abstract

In this paper, we propose a Vasicek-type of models for estimating portfolio level probability of default (PD). With these Vasicek models, asset correlation and long-run PD for a risk homogenous portfolio both have analytical solutions, longer external time series for market and macroeconomic variables can be included, and the traditional asymptotic maximum likelihood approach can be shown to be equivalent to least square regression, which greatly simplifies parameter estimation. The analytical formula for long-run PD, for example, explicitly quantifies the contribution of uncertainty to an increase of long-run PD. We recommend the bootstrap approach to addressing the serial correlation issue for a time series sample. To validate the proposed models, we estimate the asset correlations for 13 industry sectors using corporate annual default rates from S&P for years 1981-2011, and long-run PD and asset correlation for a US commercial portfolio, using US delinquent rate for commercial and industry loans from US Federal Reserve.

Suggested Citation

  • Yang, Bill Huajian, 2013. "Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models," MPRA Paper 57244, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:57244
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    References listed on IDEAS

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    1. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    2. 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.
    3. Mr. Maria Soledad Martinez Peria & Mr. Giovanni Majnoni & Mr. Matthew T Jones & Mr. Winfrid Blaschke, 2001. "Stress Testing of Financial Systems: An Overview of Issues, Methodologies, and FSAP Experiences," IMF Working Papers 2001/088, International Monetary Fund.
    4. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
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    Cited by:

    1. Yang, Bill Huajian & Yang, Jenny & Yang, Haoji, 2020. "Modeling Portfolio Loss by Interval Distributions," MPRA Paper 102219, University Library of Munich, Germany.
    2. Yang, Bill Huajian & Wu, Biao & Cui, Kaijie & Du, Zunwei & Fei, Glenn, 2019. "IFRS9 Expected Credit Loss Estimation: Advanced Models for Estimating Portfolio Loss and Weighting Scenario Losses," MPRA Paper 93634, University Library of Munich, Germany.
    3. M. Dietsch & K. Düllmann & H. Fraisse & P. Koziol & C. Ott, 2016. "Support for the SME Supporting Factor - Multi-country empirical evidence on systematic risk factor for SME loans," Débats économiques et financiers 23, Banque de France.

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    More about this item

    Keywords

    Portfolio level PD; long-run PD; asset correlation; time series; serial correlation; bootstrapping; binomial distribution; maximum likelihood; least square regression; Vasicek model;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • 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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