CDOs and Correlation: A Few Modeling Misconceptions

Since June 2007, the creditworthiness of structured finance products has deteriorated rapidly. The number of downgrades in November 2007 alone exceeded 2,000 and many downgrades were severe, with 500 tranches downgraded more than 10 notches. Massive downgrades continued in 2008. More than 11,000 of the downgrades affected securities that were rated AAA. This paper studies the credit rating crisis of 2007-2008 and in particular describes the collapse of the credit ratings of ABS CDOs. Using data on ABS CDOs we provide suggestive evidence that ratings shopping may have played a role in the current crisis. We find that tranches rated solely by one agency, and by S&P in particular, were more likely to be downgraded by January 2008. Further, tranches rated solely by one agency are more likely to suffer more severe downgrades.(This abstract was borrowed from another version of this item.)

We address the estimation of asset correlation for credit risk assessment in the Italian market and its impact on SME credit access. The empirical evidence demonstrates that assumptions underlying the regulatory capital formula are not substantiated, and benefits received from the respect of granularity could be reduced or even removed. This outcome could depend on the positive relationship between asset correlation and default probability, the negative relationship between asset correlation and size and the positive link between default correlation and default probability. The regulatory impact is that the goal of levelling the playing field could fail, a regulatory arbitrage opportunity could be created and certain firms, clustered by size and industry, could suffer from the credit crunch.

The objective of this paper is to help a bank originator of a collateralized debt obligation (CDO) to build a maximally profitable CDO. We consider an optimization framework for structuring CDOs. The objective is to select attachment/ detachment points and underlying instruments in the CDO pool. In addition to “standard” CDOs we study so-called “step-up” CDOs. In a standard CDO contract the attachment/detachment points are constant over the life of a CDO. In a step-up CDO the attachment/detachment points may change over time. We show that step-up CDOs can save about 25–35% of tranche spread payments (ie, profitability of CDOs can be boosted by about 25–35%). Several optimization models are developed from the bank originator perspective. We consider a synthetic CDO where the goal is to minimize payments for the credit risk protection (premium leg), while maintaining a specific credit rating (assuring the credit spread) of each tranche and maintaining the total incoming credit default swap spread payments. The case study is based on the time-to-default scenarios for obligors (instruments) generated by the Standard & Poor’s CDO Evaluator. The Portfolio Safeguard package by AORDA was used to optimize the performance of several CDOs based on example data.

Collateralized debt obligations (CDOs) were issued in 1987 by bankers at Drexel Burnham Lambert Inc. A decade later, CDOs became the leading power on the credit derivative markets, on which the value of derivative assets was derived from the value of other assets. However, unlike options and credit swamps, CDOs are not real, which means that they are constructed, and sometimes even the construction of their construction. CDOs were made to satisfy different types of investors, at one end, there is low-risk with low-income, and at the other, high-risk with high-income. By 2007, following the bubble burst on the US real estate market, losses on the CDO market started to expand. By 2008, the crisis on the CDO market turned into what we call today 'the global financial crisis.' CDOs are 'in the heart' of the crisis, and even wider. Our attempt is to reveal the mechanism of collateralized debt obligations (CDOs) and the way in which CDOs expanded the negative effects of the present global financial crisis.

PurposeThis 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.Design/methodology/approachThe 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.FindingsThe 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.Research limitations/implicationsThe 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.Practical implicationsThe 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.Originality/valueThe 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.

Default risk is one of the most important and fastest growing areas in derivatives. Single-name credit default swaps are now well established, and markets for contracts based on the default experience of a credit portfolio, like collateralized debt obligations (CDOs) and basket default swaps, are developing rapidly. Portfolio credit risk requires default correlation as a critical input. But defaults are rare, so default correlation must be estimated in another way, typically from correlations in stock returns. In a „structural” credit risk model, a credit event occurs when the net asset value of the firm falls below a critical threshold. Transitions among credit rating classes can be modeled with a set of thresholds corresponding to the different ratings. The widely used „normal copula” model treats the default probability for a single issuer, and default correlations among pairs of issuers, as arising from exposure to a set of common stochastic risk factors plus an idiosyncratic term. The resulting models are intuitive, but calibration to (implied) correlations embedded in market CDO prices can be difficult, especially as the number of factors increases. In this article, Overbeck and Schmidt offer an alternative structural approach that produces similar values to the normal copula model, with considerably less difficulty. Their trick is to alter the time scales of the Wiener processes driving the underlying asset values, which is equivalent to allowing time-varying volatilities, and permits a much easier calibration of the correlations.

The use of stress testing for risk monitoring has increased considerably over the last decade. Stress testing – a simulation technique used to assess the strength of a portfolio or a financial institution under unusual economic conditions – emerged as a powerful tool that was originally used in market risk. Its use has subsequently been extended into credit risk. To stress test a credit risk portfolio, practitioners focus on the key parameters that allow the risk of a credit portfolio to be assessed. These parameters, also known as Basel II parameters, are probability of default, loss given default, exposure at default and asset correlation. In this paper, using a time series approach (specifically, an error correction model), we focus on the probability of default parameter that is related to macroeconomic factors. Such an approach involves dealing with the nonstationarity of economic time series and cointegration issues. Hence, when the model is estimated, the probability of default can be simulated by measuring the effects of macroeconomic shocks applied to the model. In turn, these probabilities of default can be used to measure the impact on the probability of default under a given macroeconomic scenario, and then to improve the credit risk monitoring. The results of our study suggest that error correction models are well-suited to macroeconomic stress testing. Indeed, the fitting of the historical probability of default and the results under the stress scenarios considered here are satisfactory.

This paper uses a unique data set of more than 1000 synthetic Collateralized Debt Obligations (CDOs) deals to describe typical structures, their pricing and performance with the aim of identifying the factors behind the spectacular collapse of this important segment of structured credit market in late 2008. The data suggests that mark-to-market losses on many synthetic CDO tranches were much more significant than in case of simpler, lower-rated products despite the former experiencing little or no impairment of the notional. The losses were driven instead by the concentration of relatively limited number of defaults in a short period of time, suggesting that pre-crisis pricing must have seriously underestimated such risk of default clustering. In view of the post-crisis pick-up in synthetic CDO issuance, the paper attempts to heed this lesson and offer a simple factor model of default correlation in the spirit of Marshall–Olkin that is naturally suited to capturing the temporal dimension of default dependencies that have been crucial for synthetic CDOs investors. The model allows building a rich dependence structure capable of consistently fitting standardized iTraxx and CDX index tranches, which makes it ideal for pricing bespoke CDOs.

This paper, inspired by the efforts of a Canadian bank, discusses Basel preparation and validation issues. A comprehensive outcomes analysis (eg, back-testing) framework is presented, including a simulation-based calibration test. A consistent risk rating philosophy - point-in-time (PIT) or through-the-cycle (TTC) - encompasses both the probability of default (PD) and the default correlations, and the validation needs to be consistent with both. Related arguments are made that not only PD itself, but the correlation of PD used in economic capital models should be rating system specific. We need to use a larger PD correlation under a TTC rating system than under a PIT rating system. Furthermore, Basel loss given default may not be appropriate for commonly used internal models, and accordingly adjustments are proposed.

Cross-Market and Cross-Firm Effects in Implied Default Probabilities and Recovery Values

The main challenge of forecasting credit default risk in loan portfolios may be seen in forecasting the default probabilities and the default correlations. We derive a Merton-style threshold value model for the default probability which treats the asset value of a firm as unknown and uses a factor model instead. In addition, we demonstrate how default correlations can be easily modeled. The empirical analysis is based on a large data set of German firms provided by Deutsche Bundesbank. We find that default probabilities can be forecast given the values of risk drivers known at the point of time at which the forecast is made. In addition, correlations depend on the fit of the estimated default probabilities to the realized default rate for given points in time.

The goal of this paper is to develop the dynamic alpha (α)-stable method for collateralized debt obligation (CDO) pricing based on the α-stable distributions, which will resolve the two issues caused by using traditional static factor copula method in the practice, which means when pricing CDOs, the traditional static factor Copula method does not only exhibit the correlation smile phenomenon which is not inconsistent with the model's assumption, but also cannot be used in pricing CDOs or credit portfolio derivatives for the underlying portfolio with different maturities. As the applications, we present calibration and empirical numerical results for iTraxx Europe Tranches quotes from the market data on March 30, 2007. Thus, our new method under the framework of the dynamic α-stable model is the way for CDO pricing in the practice, and should be useful for the risk management in the practice too.

Depending on the circumstances, U.S. equity investments in collateralized debt obligations (CDOs) may be governed by the Passive Foreign Investment Company (PFIC) rules, the Controlled Foreign Company (CFC) rules, or both. The PFIC and CFC tax regimes are exceptionally nuanced and, consequently, proper tax planning depends on a careful examination of the individual circumstances of the investor and analysis of the risks of the investment. This article focuses on tax aspects of equity investments in CDOs by taxable U.S. persons and the strategies that may effectively be used to maximize certain U.S. tax benefits. The discussion focuses on the characteristics of a typical offshore CDO structure, on advantages that U.S. investors in CDO equity may obtain by making a Qualified Electing Fund election (QEF election), the circumstances in which a QEF election is not advisable, and the interplay of the PFIC and CFC rules.

This paper introduced an analytical solution and improved one-factor Gaussian copula models to the pricing of tranches of a Collateralized debt obligations (CDO) portfolio. Prices of CDO tranches are calculated and compared using the analytical model and different one-factor Gaussian copula models including a two-category heterogeneous model and a completely heterogeneous model that uses individual rate parameter and correlation coefficient for each reference entity in a CDO portfolio. When correlation among reference entities is low, the price calculated from the analytical model matches very well with the one-factor Gaussian copula models. However, as the correlation among reference entities increases, prices calculated using both the analytical solution and the homogeneous or two-category one-factor Gaussian copula models significantly deviate from the completely heterogeneous one-factor Gaussian copula model. This result verifies our belief that uniform parameters cannot completely capture all the heterogeneities in a CDO portfolio. Completely heterogeneous one-factor Gaussian copula model using individual rate parameters and correlation coefficients for each reference entities provides more reliable and accurate prices for structured securities.

In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distribution can be underestimated considerably. The problem of underestimating tail losses becomes even more severe, when calibration issues are taken into account. To demonstrate this we choose a Merton–type structural model as our reference system. Diffusion and jump–diffusion are considered as underlying processes. We run Monte Carlo simulations of this model and calibrate different recovery models to the simulation data. For simplicity, we take the default probabilities directly from the simulation data. We compare a reduced–form model for recoveries with a constant recovery approach. In addition, we consider a functional dependence between recovery rates and default probabilities. This dependence can be derived analytically for the diffusion case. We find that the constant recovery approach drastically and systematically underestimates the tail of the loss distribution. The reduced–form recovery model shows better results, when all simulation data is used for calibration. However, if we restrict the simulation data used for calibration, the results for the reduced–form model deteriorate. We find the most reliable and stable results, when we make use of the functional dependence between recovery rates and default probabilities.