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Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation

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  • Rongda Chen
  • Ze Wang

Abstract

Recovery rate is essential to the estimation of the portfolio’s loss and economic capital. Neglecting the randomness of the distribution of recovery rate may underestimate the risk. The study introduces two kinds of models of distribution, Beta distribution estimation and kernel density distribution estimation, to simulate the distribution of recovery rates of corporate loans and bonds. As is known, models based on Beta distribution are common in daily usage, such as CreditMetrics by J.P. Morgan, Portfolio Manager by KMV and Losscalc by Moody’s. However, it has a fatal defect that it can’t fit the bimodal or multimodal distributions such as recovery rates of corporate loans and bonds as Moody’s new data show. In order to overcome this flaw, the kernel density estimation is introduced and we compare the simulation results by histogram, Beta distribution estimation and kernel density estimation to reach the conclusion that the Gaussian kernel density distribution really better imitates the distribution of the bimodal or multimodal data samples of corporate loans and bonds. Finally, a Chi-square test of the Gaussian kernel density estimation proves that it can fit the curve of recovery rates of loans and bonds. So using the kernel density distribution to precisely delineate the bimodal recovery rates of bonds is optimal in credit risk management.

Suggested Citation

  • Rongda Chen & Ze Wang, 2013. "Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-9, July.
    • Handle: RePEc:plo:pone00:0068238
    DOI: 10.1371/journal.pone.0068238
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    References listed on IDEAS

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    1. Daniel Rösch & Harald Scheule, 2006. "A Multi-Factor Approach for Systematic Default and Recovery Risk," Springer Books, in: Bernd Engelmann & Robert Rauhmeier (ed.), The Basel II Risk Parameters, chapter 0, pages 105-125, Springer.
    2. repec:uts:ppaper:v:15:y:2005:i:3:p:63-75 is not listed on IDEAS
    3. Düllmann, Klaus & Trapp, Monika, 2004. "Systematic Risk in Recovery Rates: An Empirical Analysis of US Corporate Credit Exposures," Discussion Paper Series 2: Banking and Financial Studies 2004,02, Deutsche Bundesbank.
    4. Jon Frye, 2000. "Depressing recoveries," Emerging Issues, Federal Reserve Bank of Chicago, issue Oct.
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    Cited by:

    1. Can Yilmaz Altinigne & Harun Ozkan & Veli Can Kupeli & Zehra Cataltepe, 2019. "An Empirical Study on Arrival Rates of Limit Orders and Order Cancellation Rates in Borsa Istanbul," Papers 1909.08308, arXiv.org.
    2. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    3. Pawel Siarka, 2021. "Modeling Recoveries of US Leading Banks Based on Publicly Disclosed Data," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    4. Castellano, Rosella & Corallo, Vincenzo & Morelli, Giacomo, 2022. "Structural estimation of counterparty credit risk under recovery risk," Journal of Banking & Finance, Elsevier, vol. 140(C).

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