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.
Highlights
Credit risk is the distribution of financial losses caused by unexpected changes in compliance of financial agreements
The histogram of defaulted loans’ recovery rates (Fig. 2) demonstrates two peaks, where a bimodal characteristic can be seen that the probabilities of full recovery rates ranging from 0.9 to 1 and low ones from 0.1 to 0.2 are both very high
Combining the kernel density estimation curve into it, we find that the curve of the kernel density estimation has perfect fit to the distribution of the bonds’ recovery rate
Summary
Credit risk is the distribution of financial losses caused by unexpected changes in compliance of financial agreements. The recovery rate is an important measure of how much we can retrieve from bad debts. It is crucial to figure out what kind of distribution recovery rates of the sample comply with. An important key in building the credit risk model is the recovery rate in default or loss given default (LGD) function, expressed as a ratio (dollar recovery/amount invested) [1]. Research on recovery rate has mainly focused on factors that impact recovery rate, correlation between recovery rate and default rate, its distribution, etc. The influencing factors of recovery rate are more complex. The correlation between recovery rate and default rate turns out to be positive. Hu & Perraudin [3], Rosch & Scheule [4] find that it will underestimate the portfolio’s loss if the correlation is neglected
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