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Resolutions to flip-over credit risk and beyond

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  • Yang, Bill Huajian

Abstract

Given a risk outcome y over a rating system {R_i }_(i=1)^k for a portfolio, we show in this paper that the maximum likelihood estimates with monotonic constraints, when y is binary (the Bernoulli likelihood) or takes values in the interval 0≤y≤1 (the quasi-Bernoulli likelihood), are each given by the average of the observed outcomes for some consecutive rating indexes. These estimates are in average equal to the sample average risk over the portfolio and coincide with the estimates by least squares with the same monotonic constraints. These results are the exact solution of the corresponding constrained optimization. A non-parametric algorithm for the exact solution is proposed. For the least squares estimates, this algorithm is compared with “pool adjacent violators” algorithm for isotonic regression. The proposed approaches provide a resolution to flip-over credit risk and a tool to determine the fair risk scales over a rating system.

Suggested Citation

  • Yang, Bill Huajian, 2019. "Resolutions to flip-over credit risk and beyond," MPRA Paper 93389, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:93389
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    File URL: https://mpra.ub.uni-muenchen.de/93389/1/MPRA_paper_93389.pdf
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    References listed on IDEAS

    as
    1. Potharst, R. & Feelders, A.J., 2002. "Classification Trees for Problems with Monotonicity Constraints," ERIM Report Series Research in Management ERS-2002-45-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Anderson, Raymond, 2007. "The Credit Scoring Toolkit: Theory and Practice for Retail Credit Risk Management and Decision Automation," OUP Catalogue, Oxford University Press, number 9780199226405.
    3. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
    4. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    risk scale; maximum likelihood; least squares; isotonic regression; flip-over credit risk;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G3 - Financial Economics - - Corporate Finance and Governance
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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