Synthetic Collateralized Debt Obligations Research Articles

A contagion process with self-exciting jumps in credit risk applications

The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the default probability of a single firm and probability of the total number of defaults by time $t$ in a homogeneous portfolio. We use a contagion process to model the arrival of credit events causing the default and develop a framework that allows firms to have resistance against default unlike the standard intensity-based models. We assume the point process driving the credit events is composed of a systematic and an idiosyncratic component, whose intensities are independently specified by a mean-reverting affine jump-diffusion process with self-exciting jumps. The proposed framework is competent of capturing the feedback effect. We further demonstrate how the proposed framework can be used to price synthetic collateralized debt obligation (CDO). Finally, we present the sensitivity analysis to demonstrate the effect of different parameters governing the contagion effect on the spread of tranches and the expected loss of the CDO.

Commentary: Credit Rating Failures in the Aftermath of the Mortgage Meltdown

Credit ratings from the major rating agencies failed to signal the true risk content of residential mortgage-backed securities (RMBS), collateralized debt obligations (CDOs), and commercial mortgage-backed securities (CMBS) issued from 2005 through 2007. This article compares the failures across rating agencies and asset classes, using data filed by the rating agencies with the Securities and Exchange Commission (SEC). The data confirm the terrible performance of RMBS ratings. The likely causes include a combination of the breakdown of mortgage industry lending practices and the concurrent deterioration of rating agency practices. The data show that CDO ratings perform somewhat better than RMBS ratings. That result is perhaps surprising and likely reflects the confounding effects of the SEC’s definitions of its reporting categories. The data also show bad performance for CMBS ratings although the underlying causes differ from those driving the results for RMBS and CDOs. Moreover, the data show high levels of rating withdrawals across all asset classes, raising the question of possible underreporting of defaults. <b>Key Findings</b> ▪ Rating agency data reported to the SEC confirm the terrible performance of RMBS ratings, with triple-A-rated RMBS displaying 10-year default rates of 30% to 35% as of year-end 2017. The likely causes include a combination of the breakdown of mortgage industry lending and securitization practices and the concurrent deterioration of rating agency practices. ▪ The data show that CDO ratings performed better than RMBS ratings, likely because the data include ratings for many synthetic corporate CDOs. Other studies indicate that performance is significantly worse for CDOs backed by structured finance assets. ▪ CMBS ratings also performed poorly. Although CMBS rated triple-A displayed 10-year default rates of only 2% to 3%, those rated double-A had default rates of 12% to 19% while single-A-rated CMBS default rates were 23% to 32%. ▪ The data document high levels of unexplained rating withdrawals on structured finance securities. The effect of such withdrawals may be to artificially depress the reported default rates.

FACTOR COPULA MODEL FOR PORTFOLIO CREDIT RISK

A critical aspect in the valuation and risk management of multi-name credit derivatives is the modeling of the dependence among sources of credit risk. The dependence modeling poses difficulties in the pricing of a multi-name credit derivatives, in the estimation of the value-at-risk of a portfolio, or in the pricing of some other basket credit derivative as the description not only on the default arrival in an individual reference entity but on the default dependence among entities in the portfolio should be considered. Although the elliptical models have been widely used due to their mathematical tractability, the dependence modeling using the multi-dimensional Lévy process has shown growing interest among researchers despite its complexity. In this paper, we introduce one factor copula model for portfolio credit risk based on Normal Tempered Stable (NTS) distribution and calibrate the model through 5-year synthetic Collateralized Debt Obligation (CDO) tranche spreads under a large homogeneous portfolio approximation. The calibration results show that the one factor copula model based on NTS distribution is more flexible and provides a dependence structure fitting market CDO tranche spreads. As one of the major applications of the dependence modeling in credit risk, this model shares the advantage of the Gaussian one factor model, and all extensions and implementation methods used for it can be utilized.

Ethical Challenges of Complex Products: Case of Goldman Sachs and the Synthetic Collateralized Debt Obligations

In analyzing complex products, this study selected the company Goldman Sachs and one of its product offerings, the synthetic collateralized debt obligation (synthetic CDO). The study later analyzed the ethical implications of providing such a complex product to customers. A review of the literature indicates that researchers identified this product and other associated derivatives of the mortgage backed securities as the main causes of the 2008 financial crisis in the United States of America. As such, Goldman Sachs&amp;rsquo; offering of the product posed ethical and moral issues. An analysis of the company and its offering was done under the lenses of various ethical theories such as Kohlberg&amp;#39;s theory of moral reasoning, the Kantian ethics, the utilitarian perspective, Friedman&amp;rsquo;s shareholder theory, the stakeholder theory, the market approach to consumer protection, and the contract view of consumer protection. Besides Friedman&amp;rsquo;s shareholder theory, all other theories judged the product offering morally wrong and unethical. At the end of the study, the author suggested a contribution to knowledge regarding Kohlberg&amp;rsquo;s theory of moral reasoning in its application to organizations. The author also suggested further research to validate the outcome of Friedman&amp;rsquo;s shareholder theory regarding this case.

Will the Leveraged Loan Market Trigger a Financial Pandemic? Understanding Cov-Lite Loans, CLOs and EBITDA Add-Backs

Even before the coronavirus plunged the world's financial markets, analysts and regulators had been describing the $1.2 to 1.5 trillion leveraged loan market as a ticking time bomb likely to play a role in causing the next financial crisis. Many have been denouncing problematic fundamentals in the current leveraged loan market and comparing them to those that caused the 2007 subprime mortgage crisis to spread into a full-blown financial crisis towards the second half of 2008. Two legal innovations in the world of corporate finance are the main anticipated culprits of a future financial meltdown: covenant-lite (or “cov-lite”) loans and Collateralized Loan Obligations (CLOs). Our paper argues that concerns of a systemic breakdown in the financial system as a result of cov-lite loans and CLOs may be overstated. To do this, we first draw from a seminal working paper by researchers at the Federal Reserve of Philadelphia that demonstrate that cov-lite loans are almost universally part of a syndication structure that binds borrowers to compliance with financial covenants. Secondly, the paper succinctly explains CLOs and compares them with similar structured finance and securitization products, such as Collateralized Debt Obligations (CDOs), CDO-squared and CDO-cubed, as well as with derivatives, such as synthetic CDOs and Credit Default Swaps (CDSs), all of which played a role in obscuring financial market fundamentals in the lead-up to the great financial crisis. Third, the paper briefly analyzes the latest stress test results and financial stability reports by regulators in charge of monitoring systemic risk in the banking and wider financial systems. Finally, the paper explores EBITDA add-backs, a product of contract law and accounting that have played an increasing role in large Leveraged Buyout (LBO) deals and could distort a lender's credit monitoring functions, but concludes that they are currently ignored in the ratings analysis of leveraged loans and CLOs.

A set-valued Markov chain approach to credit default

We propose a novel credit default model that takes into account the impact of macroeconomic factors and intergroup contagion on the defaults of obligors. We use a set-valued Markov chain to model the default process, which includes all defaulted obligors in the group. We obtain analytic characterizations for the default process and derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.

A Markov Modulated Dynamic Contagion Process with Application to Credit Risk

Self-exciting point processes are applied to various fields such as seismology, finance, neurophysiology, criminology, biology etc to model the clustering/contagion phenomenon and extreme risk events. This article proposes an analytically tractable point process, a generalization of the classical Hawkes process, with the intensity process following a Markov modulated mean-reverting affine jump-diffusion process with contagion effects. The proposed process has both self-exciting and externally-exciting jumps that represent the effects of endogenous and exogenous events. This article derives the closed-form expressions, for distributional properties such as the first order moment, probability generating function (PGF) of the point process and Laplace transform of the intensity process, which makes it computationally efficient. The application of the proposed process to price the synthetic collateralized debt obligations (CDOs) in a top-down framework is also presented.

A Set-Valued Markov Chain Approach to Credit Default

We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.

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.

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.

Financial Market Effects of Synthetic Collateralized Debt Obligations

This paper examines the causal effect of index creation on security prices in related markets. Using a novel identification strategy, I document persistent treatment effects attributable to index inclusion. Variation in the difference between bond and credit default swap (CDS) spreads, known as the basis, is caused by variation in measures of index inclusion. Using proprietary data on the voting outcomes of the Markit CDX index formation process, I identify a persistent effect that contrasts with the predictions of existing theoretical models of the basis. Also, I document evidence of equity market contagion for firms included in a high number of credit indices.

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.

A Transactional Genealogy of Scandal: From Michael Milken to Enron to Goldman Sachs

Three scandals have reshaped business regulation over the past thirty years: the securities fraud prosecution of Michael Milken in 1988, the Enron implosion of 2001, and the Goldman Sachs “ABACUS” enforcement action of 2010. The scandals have always been seen as unrelated. This Article highlights a previously unnoticed transactional affinity tying these scandals together — a deal structure known as the synthetic collateralized debt obligation involving the use of a special purpose entity (“SPE”). The SPE is a new and widely used form of corporate alter ego designed to undertake transactions for its creator’s accounting and regulatory benefit. The SPE remains mysterious and poorly understood despite its use in framing transactions involving trillions of dollars and its prominence in foundational scandals. The traditional corporate alter ego was a subsidiary or affiliate with equity control. The SPE eschews equity control in favor of control through preset instructions emanating from transactional documents. In theory, these instructions are complete or very close thereto, making SPEs a real-world manifestation of the “nexus of contracts” firm of economic and legal theory. In practice, however, formal designations of separateness do not always stand up under the strain of economic reality. When coupled with financial disaster, the use of an SPE alter ego can turn even a minor compliance problem into a scandal because of the mismatch between the traditional legal model of the firm and the SPE’s economic reality. The standard legal model looks to equity ownership to determine the boundaries of the firm: equity is inside the firm, while contract is outside. Regulatory regimes make inter-firm connections by tracking equity ownership. SPEs escape regulation by funneling inter-firm connections through contracts, rather than equity ownership. The integration of SPEs into regulatory systems requires a ground-up rethinking of traditional legal models of the firm. A theory is emerging, not from corporate law or financial economics, but from accounting principles. Accounting has responded to these scandals by abandoning the equity touchstone in favor of an analysis in which contractual allocations of risk, reward, and control operate as functional equivalents of equity ownership — an approach that redraws the boundaries of the firm. Unfortunately, corporate and securities law hold out no prospects for similar responsiveness. Accordingly, we await the next alter-ego-based innovation from Wall Street’s transaction engineers with an incomplete menu of defensive responses.

Lemons and CDOs: Why Did so Many Lenders Issue Poorly Performing CDOs?

Collateralized Debt Obligations (CDO) played a key role in the growth of Asset-Backed Security (ABS) issuance between 2004 and 2007 by providing a mechanism for lower-rated ABS to be used as collateral for the creation of AAA securities. Using a database published by Pershing Square Capital Management covering all of the assets underlying 528 CDOs and CDO Squareds issued from 2005 through 2007 and using rating history and other information from the ABSNet database, we compare the characteristics and performance of ABS observed in a CDO with other ABS not observed in a CDO. We find that CDO assets tend to be lower rated securities from the lowest quality asset classes and vintages, and with a higher spread at issuance. CDO assets performed much worse than comparable securities that were not included in a CDO. When we control for the initial rating, CDO assets have a downgrade severity that is at least twice as bad as comparable ABS not included in a CDO. Synthetic CDOs assets perform worse than cash CDO assets, but assets included in both cash and synthetic CDOs perform worst of all (with a downgrade severity about two and one-half times worse than the average downgrade severity). Even when we include controls for a wide variety of observable characteristics, including initial yield, CDO assets still underperform comparable ABS by between 50 and 100 percent. These results suggest that CDO originators successfully sold securities and insurance against the worst performing ABS assets, but also that buyers of CDOs would have had a hard time analyzing these securities based on observable characteristics alone.

Cash Flow Optimization on Synthetic CDOs

Collateralized Debt Obligations are not as widely used nowadays as they were before 2007 Subprime crisis. Nonetheless there remains an enthralling challenge to optimize cash flows associated with synthetic CDOs. A Gaussian-based model is used here in which default correlation and unconditional probabilities of default are highlighted. Then numerous simulations are performed based on this model for different scenarios in order to evaluate the associated cash flows given a specific number of defaults at different periods of time. Cash flows are not solely calculated on a single bought or sold tranche but rather on a combination of bought and sold tranches. With some assumptions, the simplex algorithm gives a way to find the maximum cash flow according to correlation of defaults and maturities. The used Gaussian model is not realistic in crisis situations. Besides present system does not handle buying or selling a portion of a tranche but only the whole tranche. However the work provides the investor with relevant elements on how to know what and when to buy and sell. Keywords—Synthetic Collateralized Debt Obligation (CDO), Credit Default Swap (CDS), Cash Flow Optimization, Probability

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.

Pricing synthetic collateralized debt obligations based on exponential approximations to the payoff function

Pricing synthetic collateralized debt obligations based on exponential approximations to the payoff function

Optimal structuring of collateralized debt obligation contracts: an optimization approach

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.

Dual quantization for random walks with application to credit derivatives

We propose a new quantization algorithm for the approximation of inhomogeneous random walks, which are essential for the valuation of collateralized debt obligation (CDO) tranches in latent factor models. This approach is based on a dual quantization operator that shares an intrinsic stationarity and therefore automatically leads to a second-order error bound for the weak approximation. We illustrate the numerical performance of our methods for approximating the conditional tranche function of synthetic CDO products and draw comparisons to the approximations achieved by the saddlepoint method and Stein's method.