Credit risk measurement: Developments over the last 20 years

This paper traces developments in the credit risk measurement literature over the last 20 years. The paper is essentially divided into two parts. In the first part the evolution of the literature on the credit-risk measurement of individual loans and portfolios of loans is traced by way of reference to articles appearing in relevant issues of the Journal of Banking and Finance and other publications. In the second part, a new approach built around a mortality risk framework to measuring the risk and returns on loans and bonds is presented. This model is shown to offer some promise in analyzing the risk-return structures of portfolios of credit-risk exposed debt instruments.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

Selecting credit rating models: a cross-validation-based comparison of discriminatory power

In commercial banking, various statistical models for corporate credit rating have been theoretically promoted and applied to bank-specific credit portfolios. In this paper, we empirically compare and test the performance of a wide range of parametric and nonparametric credit rating model approaches in a statistically coherent way, based on a ‘real-world’ data set. We repetitively (k times) split a large sample of industrial firms’ default data into disjoint training and validation subsamples. For all model types, we estimate k out-of-sample discriminatory power measures, allowing us to compare the models coherently. We observe that more complex and nonparametric approaches, such as random forest, neural networks, and generalized additive models, perform best in-sample. However, comparing k out-of-sample cross-validation results, these models overfit and lose some of their predictive power. Rather than improving discriminatory power, we perceive their major contribution to be their usefulness as diagnostic tools for the selection of rating factors and the development of simpler, parametric models.

Corporate bond default risk: A 150-year perspective

We study corporate bond default rates using an extensive new data set spanning the 1866-2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873-1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.     

Macroeconomic Conditions, Firm Characteristics, and Credit Spreads

We study a structural model that allows us to examine how credit spreads are affected by the interaction of macroeconomic conditions and firm characteristics. Unlike most other structural models, our model explicitly incorporates equilibrium macroeconomic dynamics and models a firm's cash flow as primitive processes. Corporate securities are priced as contingent claims written on cash flows. Default occurs when the firm's cash flow cannot cover the interest payments and the recovery rate is dependent on the economic condition at default. Our model produces the following predictions: (i) credit spread is mostly negatively correlated with interest rate; (ii) credit spread yield curves are upward sloping for low-grade bonds; (iii) firm characteristics have significant effects on credit spreads and these effects also vary with economic conditions. These predictions are consistent with the available empirical evidence and generate implications for further empirical investigation.     

Growth options,macroeconomic conditions,and the cross section of credit risk

This paper develops a structural equilibrium model with intertemporal macroeconomic risk, incorporating the fact that firms are heterogeneous in their asset composition. Compared with firms that are mainly composed of invested assets, firms with growth options have higher costs of debt because they are more volatile and have a greater tendency to default during recession when marginal utility is high and recovery rates are low. Our model matches empirical facts regarding credit spreads, default probabilities, leverage ratios, equity premiums, and investment clustering. Importantly, it also makes predictions about the cross section of all these features.     

On the calibration of structural credit spread models

Empirical findings are mixed about the performance of structural models for term structure of credit spreads. It is commonly believed that all structural models have equally poor performance after calibration. However, proper calibration is not a trivial issue, especially for highly structural models. This paper proposes a more accurate procedure for calibrating two models: Leland–Toft (J Finance 51:987–1019, 1996) and Collin-Dufresne and Goldstein (J Finance 56:2177–2208, 2001). Using rating-based bond data, we find that the Leland–Toft model has significantly greater explanatory power for credit spreads across rating categories than previously reported. We provide theoretical explanations for these findings, and further extend our empirical analysis to include 286 individual senior bonds. Our findings help clarify the controversies over the performance of structural models in general and that of the Leland–Toft model in particular. In addition, we offer a rigorous procedure that can be used for calibrating other structural models more effectively.      

Recent Developments in Credit Markets

We summarize recent developments in the credit derivative markets. We show the role of dependence between individual debtors in portfolio derivatives in a study of implied correlation. The risk of changing dependence structures between stock and bond markets becomes evident in an example of capital structure arbitrage. How credit derivatives can introduce new risks is illustrated by the example of “overlay” in basket derivatives.