Abstract
In this paper, we introduce two kinds of models, beta distribution estimation and the kernel density distribution estimation, to simulate the distribution of the ultimate recovery rates of bonds. As we know, the model based on the beta distribution is common in the daily use by the investors and financial agents. However, it has a fatal defect that it can't fit the two-peaked distribution. In order to overcome this flaw, the kernel density is introduced and we compared the simulation results of these two different methods to make a conclusion that the Gauss kernel density distribution do really better imitate the distribution of the two-peaked sample with the data of the recovery rates of the municipal bonds from 1970 to 2010. Finally, we make a Chi-square test of the Gauss kernel density estimation to prove that it can fit the curve to the recovery rates of bonds. So in the future, we may consider using the kernel density distribution as a method to simulate the ultimate recovery rates of bonds with two peaks in the credit risk management.
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