On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities

In this paper we analyse recovery rates on defaulted bonds using the Stan- dard and Poor’s / PMD database for the years 1981-1999. Due to the speci…c nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametri- cally using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estima- tion on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the em- pirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We eval- uate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk. Key words : default, recovery, kernel estimation, credit risk. JEL Classi…cation : C13, C14, C51, G18, G21, G33.