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Reinforced urn processes for credit risk models

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  • Peluso, Stefano
  • Mira, Antonietta
  • Muliere, Pietro

Abstract

We propose a Bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes (RUP) introduced in Muliere et al. (2000). The estimated default probability becomes our prior information in a parametric model for the prediction of the number of bankruptcies, with the only assumption of exchangeability within rating classes. The Polya urn construction of the transition matrix justifies a Beta distributed de Finetti measure. Dependence among the processes is introduced through the dependence among the default probabilities, with the Bivariate Beta Distribution proposed in Olkin and Liu (2003) and its multivariate generalization.

Suggested Citation

  • Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:1-12
    DOI: 10.1016/j.jeconom.2014.08.003
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    Cited by:

    1. Cheng, Dan & Cirillo, Pasquale, 2018. "A reinforced urn process modeling of recovery rates and recovery times," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 1-17.
    2. Dan Cheng & Pasquale Cirillo, 2019. "An Urn-Based Nonparametric Modeling of the Dependence between PD and LGD with an Application to Mortgages," Risks, MDPI, vol. 7(3), pages 1-21, July.
    3. Souto Arias, Luis A. & Cirillo, Pasquale, 2021. "Joint and survivor annuity valuation with a bivariate reinforced urn process," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 174-189.
    4. Tarun Chitra & Alex Evans, 2020. "Why Stake When You Can Borrow?," Papers 2006.11156, arXiv.org.
    5. Andrea Arfè & Stefano Peluso & Pietro Muliere, 2021. "The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 1-15, April.

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    More about this item

    Keywords

    Default rate estimation; Multivariate Beta distribution; Polya urn; Rating migration matrix estimation; Reinforced urn processes;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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