On the way to recovery: A nonparametric bias free estimation of recovery rate densities

Abstract

In this paper we analyse recovery rates on defaulted bonds using the Standard 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 nonparametrically 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 estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.

Predicting bank loan recovery rates with a mixed continuous‐discrete model

“…On the contrary, our parametric model cannot exhibit local modes in the interval (0,1), as many empirical studies have shown (e.g., ). For this reason, a future development of the model, here proposed, could be to assume that the continuous part of the recovery rate is a mixture of beta random variables.…”

“…Most empirical research focuses on modeling and estimating default probabilities, whereas only recently, the recovery analysis is attracting attention. Several studies consider recovery rates on corporate bonds (e.g., ), whereas some authors deal with bank loans (e.g., ). Because loans are private instruments, few data are available.…”

“…A pivotal characteristic of the recovery rate distribution is the high concentration of data at total recovery and total loss, as shown by . Hence, the estimates of total loss and total recovery are crucially important for banks.…”

Modeling Ultimate Loss Given Default on Corporate Debt

“…7 Alternatives in the literature having different advantages and disadvantages relative to our approach, which we find to yield similar results on this dataset, include non-parametric approaches (Renault and Scailett [2003]) or maximumentropy (Friedman and Sandow [2003]). …”

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

“…As competitors of the models in our family we consider some of the non‐parametric approaches for density estimation discussed in Section 2. They are (a)GK, the Gaussian kernel that was considered by Renault and Scaillet () and Chen and Wang (), (b)H‐BK, the semiparametric density that was considered by Hagmann et al . (), (c)C‐BK, the beta kernel that was introduced by Chen (), and applied by Renault and Scaillet (), and (d)CZ‐BK, the beta kernel that was proposed by Calabrese and Zenga (). …”