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.

Recovery Rates of Bank Loans: Empirical Evidence for Germany

“…In figure 2, the borrowers are ordered starting with the borrower that exhibits the lowest recovery rate. 44 This finding supports the critique of Renault and Scaillet (2004) on the commonly assumed beta distribution used in credit risk models. After the weighting of the recovery rates with their exposure at default the mean value yields to 71.91.…”

“…Whereas for bonds the recovery rate amounts on average to 11 We only consider empirical studies that analyze the recovery rate at the time of default. 12 However, Renault and Scaillet (2004) show that the density function of bond recovery rates cannot be described only knowing the mean value and the variance. They identify density functions of recovery rates and discuss methods for the non-parametric estimation of the distribution.…”

“…Renault and Scaillet (2004) show the extent of estimation errors that arises if the usually assumed beta distribution is used for the value-at-risk calculation. 21 The second group of studies discusses the assumption of independence between the probability of the borrower's default and its recovery rate.…”

Loss Given Default for residential real estate banks: Evidence from the Euro area

“…The main aspect of the contract that can affect the recovery process results is the loan's seniority and the LGD is normally lower for more senior and secured exposures (Renault and Scaillet, 2004) and even more so for market financing solutions (Mora, 2012). Riskier financial contracts are revolving loans, where, near default, borrowers normally tend to increase their usage ratio and the lender's exposure (Zaniboni et al, 2013).…”

Improvements in Loss Given Default Forecasts for Bank Loans

“…LGD models that seek to estimate the distribution of LGDs for credit portfolio modeling are Renault and Scaillet (2004) and Calabrese and Zenga (2010).…”