Abstract
This paper analyzes the impact of various assumptions about the association between aggregate default probabilities and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects on mandatory capital requirements like those proposed in 2001 by the Basel Committee on Banking Supervision. We present the analysis and results in four distinct sections. The first section examines the literature of the last three decades of the various structural-form, closed-form and other credit risk and portfolio credit value-at-risk (VaR) models and the way they explicitly or implicitly treat the recovery rate variable. Section 2 presents simulation results under three different recovery rate scenarios and examines the impact of these scenarios on the resulting risk measures: our results show a significant increase in both expected and unexpected losses when recovery rates are stochastic and negatively correlated with default probabilities.
In section 3, we empirically examine the recovery rates on corporate bond defaults, over the period 1982-2000. We attempt to explain recovery rates by specifying a rather straightforward statistical least squares regression model. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities. Our econometric univariate and multivariate time series models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. Finally, in Section 4 we analyze how the link between default probability and recovery risk would affect the procyclicality effects of the New Basel Capital Accord, due to be released in 2002. We see that, if banks use their own estimates of LGD (as in the “advanced†IRB approach), an increase in the sensitivity of banks’ LGD due to the variation in PD over economic cycles is likely to follow. Our results have important implications for just about all portfolio credit risk models, for markets which depend on recovery rates as a key variable (e.g., securitizations, credit derivatives, etc.), for the current debate on the revised BIS guidelines for capital requirements on bank credit assets, and for investors in corporate bonds of all credit qualities.
Introduction
Credit risk affects virtually every financial contract. Therefore the measurement, pricing and management of credit risk has received much attention from financial economists, bank supervisors and regulators, and from financial market practitioners. Following the recent attempts of the Basel Committee on Banking Supervision (1999, 2001a) to reform the capital adequacy framework by introducing risk-sensitive capital requirements, significant additional attention has been devoted to the subject of credit risk measurement by the international regulatory, academic and banking communities. This paper analyzes the impact of various assumptions on which most credit risk measurement models are presently based: namely, it analyses the association between aggregate default probabilities and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects of this relationship on credit VaR models, as well as on the procyclicality effects of the new capital requirements proposed in 2001 by the Basel Committee. Before we proceed with empirical and simulated results, however, the following section is dedicated to a brief review of the theoretical literature on credit risk modeling of the last three decades.
The Relationship Between Default Rates and Recovery Rates in Credit Risk Modeling: a Review of the Theoretical and Empirical Literature
Credit risk models can be divided into two main categories: (a) credit pricing models, and (b) portfolio credit value-at-risk (VaR) models. Credit pricing models can in turn be divided into three main approaches: (i) “first generation†structural-form models, (ii) “second generation†structural-form models, and (iii) reduced-form models. These three different approaches, together with their basic assumptions, advantages, drawbacks and empirical performance, are briefly outlined in the following paragraphs. Credit VaR models are then examined. Finally, the more recent studies explicitly modeling and empirically investigating the relationship between the probability of default (PD) and recovery rates (RR) are briefly analyzed.