Yang, Bill Huajian
(2019):
*Resolutions to flip-over credit risk and beyond.*
Published in: Big Data and Information Analytics
, Vol. 3, No. 2
(18 March 2019): pp. 54-67.

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MPRA_paper_93389.pdf Download (284kB) |

## Abstract

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.

Item Type: | MPRA Paper |
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Original Title: | Resolutions to flip-over credit risk and beyond |

Language: | English |

Keywords: | risk scale, maximum likelihood, least squares, isotonic regression, flip-over credit risk |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C80 - General G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation G - Financial Economics > G1 - General Financial Markets > G18 - Government Policy and Regulation G - Financial Economics > G3 - Corporate Finance and Governance G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill G - Financial Economics > G3 - Corporate Finance and Governance > G35 - Payout Policy |

Item ID: | 93389 |

Depositing User: | Dr. Bill Huajian Yang |

Date Deposited: | 22 Apr 2019 18:47 |

Last Modified: | 29 Sep 2019 22:42 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/93389 |