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.
References
[1]
Arnaud DS, Olivier R (2004) Measuring and Managing the Credit Risk. New York: McGraw-Hill Companies.
[2]
Wang GD, Zhan YR (2011) The double Beta model of recovery rate in credit risk management. Chinese Journal of Management Science 6 (12): 10–14.
[3]
Hu Y, Perraudin W (2002) The dependence of recovery rates and defaults. Working paper, Birkbeck College.
[4]
Rosch D, Scheule H (2005) A multifactor approach for systematic default and recovery risk. The Journal of Fixed Income 15(2): 63–75.
[5]
Qu WJ, Xiong GJ (2011) Analysis and Application Research on Nonparametric Density Estimation. Journal of Shengyang Agriculture University 9: 468–472.
[6]
Chen MZ, Chen H, Ma YC, Wang B, Tang Y, et al. (2011) Recovery rate Models Based on General Beta Regression for Non-performing Loan. Journal of Applied Statistics and Management 30(5): 810–823.
Pykhtin M (2003) Unexpected recovery risk. Risk 8: 74–78.
[9]
Andersen L, Sidenius J (2004) Extension to the Gaussian Copula: Random recovery and random factor loadings. Journal of Credit Risk 1(1): 29–70.
[10]
Dullmann K, Trapp M (2004) Systematic risk in recovery rates an empirical analysis of US corporate credit exposures. Working paper: 2.
[11]
Liu HZ, He WZ (2010) Kernel density estimation of stock returns distribution and Monte Carlo simulation test- comparison study based on data after the introduction of price limit system. The world economy 2: 46–55.
[12]
Zhen ZY, Li J (2011) Application of nonparametric kernel density estimation in the Hang Seng index yield distribution. Statistics and decision 9: 22–24.
[13]
Shi ZL, Huang ZH (2009) Dynamic analysis of China provincial economy increase based on kernel density estimation. Economic survey 4: 60–63.
[14]
Camblor PM, Alvarez JD, Corral N (2008) K-Sample test based on the common area of kernel density estimators. Journal of statistical planning and inference 138: 4006–4020.
[15]
Sharon O, David C, Albert M (2011) Corporate Default and Recovery Rates, 1920–2010. Moody’s investors service: 18–21.
[16]
Sharon O, David C, Albert M (2012) Corporate Default and Recovery Rates, 1920–2011. Moody’s investors service: 23–25.
[17]
Martin LH (1999) An optimal local bandwidth selector for kernel density estimation. Journal of Statistical Planning and Inference 77: 37–50.
[18]
Mugdadia AR, Ibrahim A (2004) A bandwidth selection for kernel density estimation of functions of random variables. Computational Statistics & Data Analysis 47: 49–62.
[19]
Su JM, Zhang LH (2004) Application of Matlab tool kit. Beijing: Publishing House of Electronics Industry.
