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This chapter analyses the ability of some structural models to predict corporate bankruptcy. The study extends the existing empirical work on default risk in two ways. First, it estimates the expected default probabilities (EDPs) for a sample of bankrupt companies in the USA as a function of volatility, debt ratio, and other company variables. Second, it computes default correlations using a copula function and extracts common or latent factors that drive companies’ default correlations using a factor-analytical technique. Idiosyncratic risk is observed to change significantly prior to bankruptcy and its impact on EDPs is found to be more important than that of total volatility. Information-related tests corroborate the results of prediction-orientated tests reported by other studies in the literature; however, only a weak explanatory power is found in the widely used market-to-book assets and book-to-market equity ratio. The results indicate that common factors, which capture the overall state of the economy, explain default correlations quite well.

This paper is a first attempt to empirically calibrate the default and asset correlation for large companies in India and elaborate its implications for credit risk capital estimation for a bank.

The authors estimate default probabilities and default correlations of long‐term bonds of 542 Indian corporates using rating transitions and pair‐wise migrations over ten year cohorts of firms. Further, the implicit asset correlation from the estimated default correlations and default thresholds are derived using the asymptotic single risk factor approach.

The authors find evidence that default correlations are time variant and vary across rating grades and industries. The highest correlations are observed between companies within the same rating grades (systematic risk impact) and within the same industry (industry specific impact). More interestingly, significantly smooth monotonic relationship between the probability of default (PD) and asset correlation as prescribed by the Basel II IRB document (2006) are not found. Moreover, it is found that the asset correlation range for Indian corporates do not match with what is prescribed for corporate exposures by BCBS.

The authors address the dilemma implied by the negative relationship between PD and asset correlation as suggested by BCBS IRB formula and other research for developed economies with estimates of asset correlation for and emerging market like India and demonstrate its implications on the estimation of credit risk capital.

Estimation of default and asset correlation is crucial for banks to manage and measure portfolio credit risk. The purpose of this paper is to find empirical relationship between the default and asset correlation with default probability, to understand the effect of systematic risk.

The authors have estimated single default and implicit asset correlations for banks and corporates in India and compare it with global scenario. This paper deduces a simple methodology to estimate the default correlations from the variance of temporal default rates. Next, the asset correlations have been estimated analytically by decomposition of variance equation in Merton's one factor risk model following approaches of Gordy and of Bluhm and Overbeck.

The authors empirically find a negative relationship between asset correlation and the probability of default using Moody's global corporate data that support Basel II internal ratings‐based (IRB) correlation prescription. However, they do not find any smooth relationship between the probability of default (PD) and asset correlation for Indian corporate. The magnitude of correlation estimates based on a large bank's internal rating‐wise default rates are much lower than what is prescribed by the Basel committee. Thus, the standardized correlation figures as assumed by the Basel Committee on Banking Supervision need to be properly calibrated by the local regulators before prescribing their banks to calculate IRB risk weighted assets.

These correlation estimates will help the regulators, insurance firms and banks to understand the linkage between counterparty default risks with the systematic factors. The findings of this paper could be used further in estimating portfolio economic capital for large corporate exposures of banks and insurance companies.

Credit migration correlation is a critical assumption for the integration of market risk and credit risk within enterprise‐wide risk management. This article describes hypothesis testing performed on credit migration correlation, based on two models: 1) a factor model and 2) an asset‐value model. These tests involve both the correlation between obligors and the correlation between credit migration events and systematic market risk factors. The author concludes from the test results that over shorter risk horizons (e.g., biweekly or monthly) where all relevant underlying processes are distributed multi‐variate normal, non‐zero positive correlation weights overestimate risk capital requirements, on average.

This paper studies the pricing of collateralized debt obligation (CDO) using Monte Carlo and analytic methods. Both methods are developed within the framework of the reduced form model. One-factor Gaussian Copula is used for treating default correlations amongst the collateral portfolio. Based on the two methods, the portfolio loss, the expected loss in each CDO tranche, tranche spread, and the default delta sensitivity are analyzed with respect to different parameters such as maturity, default correlation, default intensity or hazard rate, and recovery rate. We provide a careful study of the effects of different parametric impact. Our results show that Monte Carlo method is slow and not robust in the calculation of default delta sensitivity. The analytic approach has comparative advantages for pricing CDO. We also employ empirical data to investigate the implied default correlation and base correlation of the CDO. The implication of extending the analytical approach to incorporating Levy processes is also discussed.

This analysis asks whether regulatory capital requirements capture differences in systematic risk for large firms and micro-, small- and medium-sized enterprises (MSMEs). The authors explore whether bank capital regulations intended to support SMEs’ access to borrowing are effective. The purpose of this paper is to find out whether the regulatory design (particularly the estimate of asset correlations) positively affects the lending process to small and medium enterprises, compared to large corporates.

The authors investigate the appropriateness of bank capital requirements considering default risk of loans to MSMEs and distortions in capital charges between MSMEs and large firms under the Basel III framework. The authors compiled firm-level data to capture the proportions of MSMEs and large firms in Italy during 2000–2014. The data set is drawn from financial reports of 708,041 firms over 15 years. Unlike most empirical studies that correlate assets and defaults, this study assesses a firm’s creditworthiness not by agency ratings or by sampling banks but by a specific model to estimate one-year probabilities of default.

The authors found that asset correlations increase with firms’ size and that large firms face considerably greater systematic risk than MSMEs. However, the empirical values are much lower than regulatory values. Moreover, when the authors focused on the MSME segment, systematic risk is rather stable and varies significantly with turnover. This analysis showed that the regulatory supporting factor represents a valuable attempt to treat MSME loans more fairly with respect to banks’ capital requirements. Basel III-internal ratings-based approach results show that when the supporting factor is applied, the Risk-Weighted-Assets (RWA) differences between MSMEs and large firms increase.

The implications of this research is that banking regulators to make MSMEs support more effective should review asset correlation estimation criteria, refining the fitting with empirical evidence.

The asset correlation parameter stipulated by the Basel framework is invariant with economic cycles, decreases with borrowers’ probability of default and increases with borrowers’ assets. The authors found that those relations do not hold. This way, asset correlations fall below parameters defined by regulatory formula, and SMEs’ credit risk could be overstated, resulting in a capital crunch.

The original contribution of this paper is to demonstrate that the gap between empirical and regulatory capital charge remains high. When the authors examined the Basel III-IRBA, results showed that when the supporting factor is applied, the RWA differences between MSMEs and large firms increase. This is particularly strong for loans to small- and medium-sized companies. Correctly calibrating asset correlations associated with the supporting factor eliminates regulatory distortions, reducing the gap in capital charges between loans to large corporate and MSMEs.

A major topic in retail lending is the measurement of the inherent portfolio credit risk. The needs for a better understanding and dealing with default risky securities have been reinforced by the Basel Committee on Banking Supervision [1999a, 1999b, 2000, 2001a, 2001b, 2002, 2003] which has proposed a revision of the standards for banks' capital requirements.

Credit derivatives continue to grow in popularity as well as complexity. While single‐name credit default swaps are still the most popular instruments, second‐generation products have become more commonplace. Second generation products are those whose payoffs are contingent on the viability of a number of firms and include instruments such as default baskets and synthetic collateralized debt obligations. The purpose of this paper is to provide a transparent and detailed account of default basket valuation along with thorough and intuitive explanations of comparative statics and the relationship between basket values and default correlation.

The paper delineates the standard approach to valuing default baskets and with its implementation examines results for two copula functions and the input assumptions which are critical to the valuation process.

It is found that the assumptions are critical to the valuation and that the copula chosen also has an impact on pricing and comparative statics.

This paper is very practical in its orientation and takes a pedagogical approach in its explanation of default baskets, the standard model, and key assumptions.

This paper fills a gap in the literature as prior works are more focused on certain enhancements or nuances of modeling basket credit derivatives while this work centers on the standard model and provides a thorough analysis and explanation of the comparative statics as well as a discussion of model limitations. This paper is ideal reading for those that seek an understanding of the modeling and risks associated with multi‐name credit derivatives.

This article discusses factor models for portfolio credit. In these models, correlations between individual defaults are driven by a few systematic factors. By conditioning on these factors, defaults observed within are independent. This allows a greater degree of analytical tractability in the model with a realistic dependency structure.

The implementation of credit risk models has largely relied either on the use of historical default dependence, as proxied by the correlation of equity returns, or on risk neutral equicorrelation, as extracted from CDOs. Contrary to both approaches, the purpose of this paper is to infer risk neutral dependence from CDS data, taking counterparty risk into consideration and avoiding equicorrelation. The impact of risk neutral correlation on the fees of some higher dimensional credit derivatives is also explored.

Copula functions are used in order to capture dependency. An application to market data is provided.

Both in the FtD and CDO cases, using (the correct) risk neutral measure instead of equity dependency has the same effect as the adoption of a copula with tail dependency instead of a Gaussian one. This should be important for those who resort to copulas in credit derivative pricing.

As far as is known, several attempts have been made in order to compare the behavior of different copulas in derivative pricing; however, no attempt has been made in order to extract risk neutral dependence without using the equicorrelation assumption. Therefore no attempt has been made to understand which copula features could proxy for risk neutrality, whenever risk neutral dependency cannot be inferred (for instance because CDS involving that name are not actively traded)