Collateralized Debt Obligations Tranches Research Articles

A comparative analysis of ex ante credit spreads: Structured finance versus straight debt finance

This paper examines the pricing of structured finance (SF) – asset-backed securities (ABS), mortgage-backed securities (MBS), and collateralized debt obligations (CDO) – and straight debt finance transactions. Using a cross-section of 24,525 European bonds issued by financial and nonfinancial firms in the 2000–2016 period, we show that although ratings are the most important pricing determinant for SF and corporate bonds (CB) at issuance, investors rely on other contractual, macroeconomic, and firms’ characteristics beyond these ratings. We find that CDO tranches have, on average, higher credit spreads than similarly rated CB, while investors are not compensated for facing higher systematic risk components in relation to investment-grade ABS and MBS. Our results also support the hypothesis of SF transactions as mechanisms of reducing funding costs: SF transactions’ weighted average spread is lower than that of comparable CB and originating firms’ creditworthiness does not deteriorate when compared to a sample of matched firms.

HEDGING OF SYNTHETIC CDO TRANCHES WITH SPREAD AND DEFAULT RISK BASED ON A COMBINED FORECASTING APPROACH

Hedging of credit derivatives, especially the Collateralized Debt Obligations (CDOs), is the prerequisite of risk management in financial market. Since both spread risk and default risk exist, the models in existing literature resort to the incomplete-market theory to derive the hedging strategies. From another point of view, the construction of hedging strategies of CDO might be regarded as the process of forecasting the changes in value of CDO by the changes in value of hedging instruments. Based on this idea, this paper proposes an alternative hedging approach via the combined forecasting and regression techniques, where the two individual forecasting models are Gaussian copula model and local intensity model, used to hedge against spread risk and default risk, respectively. Finally, the dynamic hedge ratios of CDO tranches with CDS index are derived. A numerical analysis is carried out and the hedge ratios obtained by the new models are compared with those from actual market spreads. It is shown that the model derived in this paper not only provides hedging strategies which agree with the market hedge ratios but that can be effectively implemented as well.

Model specification and collateralized debt obligation (mis)pricing

Complex structured products, especially collateralized debt obligations (CDOs), were at the center of the 2008 credit crisis. This paper explores the impact of modeling difficulties on CDO mispricing. Comparing pricing outputs among models with different specifications, we show that the use of a model with advanced default correlation assumptions could have reduced the amount of model‐implied AAA‐rated CDO securities. This pricing difference also has predictive power for the subsequent downgrading of AAA‐rated CDO tranches. However, the model specification is only qualitatively important for CDO mispricing, as it has a modest quantitative effect in explaining the overall pricing errors.

RISE AND FALL OF SYNTHETIC CDO MARKET: LESSONS LEARNED

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.

Introducing an analytical solution and an improved one-factor gaussian copula model for the pricing of heterogeneous CDOs

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.

Hedging default risks of CDO tranches in non-homogeneous Markovian contagion models

The paper is concerned with the hedging of credit derivatives, in particular synthetic collateralized debt obligations (CDOs) tranches and first to default swap (FTD) with respect to actually traded credit default swaps index (CDS index). In the model, we will relax the name homogeneity assumption, that all the names share the same risk-neutral default. We think of two homogeneous groups of names and the default intensities of each group depending both upon the number of survived names in each subgroup. This results a two dimensional Markov chain setting, since the portfolio state is characterized by the number of survived names in each group. Finally, we have achieved the numerical implementation through trinomial trees, by means of Markov chain techniques. The experimental results show that the new extended hedge model in this paper improves the hedge strategies under the name homogeneity case.

On the Stability of Synthetic CDO Credit Ratings

AbstractSynthetic collateralized debt obligations (CDOs) performed very badly during the subprime crisis: they suffered massive rating downgrades (even at the most senior levels of the capital structure) and inflicted significant losses on investors. Using numerical simulations, this study shows that such structures are highly unstable; minor errors in the basic assumptions could manifest dramatically in the accuracy of CDO rating calculations. Regardless of the quality of the underlying assets, it is impossible to make reliable statements regarding the future performance of a synthetic CDO tranche. Moreover, this study demonstrates that single‐point credit risk estimators (in which no attempt at specifying a confidence interval is made) could be especially misleading. Finally, the study suggests that a regulatory framework based on credit ratings as they are presently defined is unlikely to be effective.

A Little Knowledge Is a Dangerous Thing: Model Specification, Data History, and CDO (Mis)Pricing

Complex structured products especially collateralized debt obligations (CDOs) were at the center of the recent credit crisis. This paper explores two structural sources of CDO mispricing: modeling difficulty and data limitation. Comparing pricing outputs among models with different specifications, we find that using model with advanced default correlation assumptions and adequate data inputs can reduce the amount of model-implied AAA-rated CDO securities by 13% on average. This pricing difference has predictive power for the subsequent downgrading of AAA rated CDO tranches. These results indicate that CDO mispricing can be partly, but not fully, attributed to model misspecifications, as well as limited availability of historical data on CDO collateral assets.

Efficient wavelets-based valuation of synthetic CDO tranches

We present new formulae for the valuation of synthetic collateralized debt obligation (CDO) tranches under a one-factor model. These formulae are based on the wavelet theory and the method used is called WA[a,b]. We approximate the cumulative distribution function (CDF) of the underlying pool by a finite combination of jth order B-spline basis, where the B-spline basis of order zero is typically called a Haar basis. We provide an error analysis and we show that for this type of distributions, the rate of convergence in the approximation is similar regardless of the order of the B-spline basis employed. The resulting formula for the Haar basis case is much easier to implement and performs better than the formula for the B-spline basis of order one in terms of computational time. The numerical experiments confirm the impressive speed and accuracy of the WA[a,b] method equipped with a Haar basis, independently of the inhomogeneity features of the underlying pool. The method appears to be particularly fast for multiple tranche valuation.

Modeling Correlation Structure for Collateralized Debt Obligations

Pricing complex financial derivatives such as collateralized debt obligations (CDO) is considered as the main reason triggering the 2008 financial crisis. The correlation structure related to the credit risks involved in a portfolio for pricing issues have been tried to overcome via a Gaussian copula framework first introduced by David Li (2000). This approach regards the correlation among the credit risks as normally distributed (tied with a Gaussian copula framework), enabling us to derive analytical solutions. However, despite its simplicity, this approach is far from reality, which caused mispricing of the tranches of CDOs. This phenomenon is called the correlation smile. This paper takes the correlation smile issue by considering a Levy copula framework. When this is introduced to pricing equations, one can see that the correlation smile is “corrected”. Thus, a more accurate model of pricing the above-mentioned tranches is introduced.

The impact of collateralized debt obligation arbitrage on tranching and financial leverage of structured finance securities

For several years leading up to the outbreak of the financial crisis, growth in the use of arbitrage collateralized debt obligations (CDOs) was explosive. In this paper, we discuss potential sources of such arbitrage opportunities, in particular, potential gains due to "bond-like pricing". For this purpose, we examine the risk profiles of CDOs in some detail, which reveals significant differences between CDO tranches and corporate bonds, in particular concerning a considerably increased sensitivity to systematic risks. Treating the structured products as singlename instruments allows us to quantify these differences. We then price CDO tranches approximately with the Merton model, similar to corporate bonds. Using a sample CDO portfolio, we describe some opportunities for "CDO arbitrage" when investors consider corporate and CDO bonds as substitute investments and use bond-like pricing. We then discuss how tranches with high systematic risk can be generated and how CDO arrangers can exploit this to their advantage. It comes as no surprise that precisely these types of structures featured in many of the CDOs issued prior to the outbreak of the financial crisis.

Analysis of Systematic Risks in Multi-Name Credit and Equity Markets

In this paper, we present an intensity-based common factor model that is used to analyze the valuation of common systematic risks in multi-name credit and equity markets. In particular, we use a hybrid intensity model to price single-name credit instruments such as credit default swaps (CDSs), multi-name credit derivatives such as collateralized debt obligations (CDOs), and equity index options such as calls and puts on the S&P 500. Once we have the expressions for the model prices of these instruments, we then calibrate the model parameters to fit the market data. We study two problems, the “forward” and “backward” problems: in the former, we start from equity index options and then compute the CDO tranche spreads, while in the latter, we fit the parameters to the CDO tranche spreads and then compute the equity index option prices and implied volatilities. We find that, based on our hybrid model, the systematic risks in the two markets were similar from 2004 to 2007, while the credit market incorporated far greater systematic risk than the equity market during the financial crisis from 2008 to 2010.

Anatomy of ABS CDO: Why Do ABS CDOs Exist?

This paper investigates the ABS CDOs (Asset-Backed Security Collateralized Debt Obligations) market between 2005 and 2007 and answers the question of why ABS CDOs exist. The dataset used in this paper contains 516 ABS CDOs, 4,023 CDO tranches, and 79,724 securities used as the collateral of ABS CDOs. Using detailed collateral information on ABS CDOs, I find that there is a large re-securitization rate distinction between AAA- and non AAA-rated tranches. Less than 1% of AAA-rated subprime MBS tranches were used as collateral for cash flow ABS CDOs. In contrast, more than half of non AAA-rated subprime tranches were re-securitized through cash flow CDO.I also show that the reference portfolio of synthetic CDOs consists to a large degree of BBB rated subprime mortgage backed securities. As a notional amount, $94 billion out of $172 billion, which was the total collateral amount of synthetic CDOs, was comprised of BBB-rated subprime MBS tranches. It is evident that the synthetic CDO market deteriorated due to short demand in the housing sector, but there is no evidence that the cash flow ABS CDO market deteriorated between 2005 and 2007.

What Went Wrong? Examining Moody’s Rated CDO Data

The downgrading of the tranches of Collateralized Debt Obligation (CDO) products backed by real estate related assets has caused severe disruptions in the housing and financial markets. The rating agencies have been criticized for the opacity in the rating process of the CDO products and also for giving the CDO tranches higher ratings than they deserved. However, not enough attention has been paid to the decision making process of the agencies to downgrade the CDO tranches. We use data from Moody’s CDO database to reconstruct the process through which Moody’s eventually downgraded the tranches. We use a discrete hazard rate model to study the variables that were relevant in the downgrading of the tranches of the CDOs. The empirical results show that out of the many CDO specific variables relevant to their ratings made available by Moody’s few have any explanatory power beyond the Moody’s Deal Scores (MDS). We show that the MDS could be explained by the changes in the Case-Shiller Composite-20 Index and Markit ABX.HE indices. Further analysis shows that Moody’s mostly relied on the changes in the Case-Shiller indexes in revising the MDS.

Pricing Synthetic CDOs Using a Three Regime Random-Factor-Loading Model

Synthetic Collateralized Debt Obligations (CDOs) were among the driving forces of the rapid growth of the market for credit derivatives in recent years. Possibly the most popular model beside the Gaussian copula for pricing CDO tranches is the Random-Factor-Loading-Model of Andersen and Sidenius (2005). We extend this model by allowing more than two regimes of default correlations. The model is calibrated to market spreads at times of financial distress and during calm periods. For both points in time the model correlation skews are similar to the steep skews observed in the market and lead to an improvement to the standard Random-Factor-Loading-Model.

CDO Squareds: The Case of Subprime Mortgages

Investment in residential subprime mortgages through structured products was at the heart of the financial crisis that began in 2007. Perhaps the most toxic such product was the CDO-squared. CDO-squareds are CDOs (collateralized debt obligations) with tranches of other CDOs serving as their collateral pool. CDO-squareds on mortgage-backed securities (ABS-CDOs) issued vast quantities of AAA rated securities that quickly fell to market values of a few cents on the dollar. This article examines ABS-CDOs with two primary purposes. First, it provides an intuitive explanation of ABS-CDOs, including their characteristics, risks, and models. Second, it performs a comprehensive sensitivity analysis of the AAA senior tranche width with respect to various parameters based on the Hull and White model of mortgage-backed securities. The authors find that ABSCDO senior tranche widths were unreasonable prior to the financial collapse that began in 2007, and they attribute the associated rating errors with the non-linearity, hyper-sensitivity, and complexity of the risks of the products with respect to their underlying parameters. Simply put, there is no reliable basis on which accurate measurements of risk can be made using existing data and theory. <b>TOPICS:</b>Asset-backed securities (ABS), CLOs, CDOs, and other structured credit

Dynamic Hedging of Portfolio Credit Derivatives

We compare the performance of various hedging strategies for index collateralized debt obligation (CDO) tranches across a variety of models and hedging methods during the recent credit crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic models do not necessarily perform better than static models, nor do high-dimensional bottom-up models perform better than simpler top-down models. When it comes to hedging, top-down and regression-based hedging with the index provide significantly better results during the credit crisis than bottom-up hedging with single-name credit default swap (CDS) contracts. Our empirical study also reveals that while significantly large moves—“jumps”—do occur in CDS, index, and tranche spreads, these jumps do not necessarily occur on the default dates of index constituents, an observation which shows the insufficiency of some recently proposed portfolio credit risk models.

Structural jump-diffusion model for pricing collateralized debt obligations tranches

This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.

The valuation of correlation-dependent credit derivatives using a structural model

In 1976, Black and Cox proposed a structural model in which an obligor defaults when the value of its assets hits a certain barrier. In 2001, Zhou showed that the model can be extended to two obligors whose assets are correlated. In this paper we show that the model can be extended to a large number of different obligors. The correlations between the assets of the obligors are determined by one or more factors. We examine the dynamics of credit spreads implied by the model and explore how the model prices tranches of collateralized debt obligations (CDOs). We compare the model with the widely used Gaussian copula model of survival time and test how well the model fits market data on the prices of CDO tranches. We consider three extensions of the model. The first reflects empirical research showing that default correlations are positively dependent on default rates. The second reflects empirical research showing that recovery rates are negatively dependent on default rates. The third reflects research showing that market prices are consistent with heavy tails for both the common factor and the idiosyncratic factor in a copula model.

Model Risk and the Design of CDO Tranches

The goal of this paper is to explore the model risk inherent in the rating and design of structured finance products. We seek to illustrate the consequences of neglecting state-dependent correlations on the methodologies and criteria employed by the major ratings agencies. In contrast to related studies, we focus exclusively on asymptotic analysis. A variety of tractable asymptotics are derived for “first-generation” securitizations, such as asset-backed securities (ABS), as well as “second-generation” securitizations, such as collateralized debt obligations (CDO) backed by tranches of ABS. Consistent with the recent work of Hull and White [2009], who explore alternative sources of model risk, we find that in the case of first-generation securitizations, the implications are substantial but not catastrophic; in the case of second-generation securitizations, however, the implications are dire. This is due to the fact that our analysis provides a parsimonious description of thin mezzanine tranches as “nearly binary” assets which tend to “go bad” at the same time; a phenomenon which is notably absent in the notorious (and industry standard) Gaussian factor models.