Senior Tranches Research Articles

Fine-Tuning the Equivalent Strike Framework for Bespoke CDO Pricing

This paper presents a fine-tuning of some mapping functions used in the Equivalent Strike framework. This new approach provides an equivalent strike that is independent from the index base correlation. This feature is valuable when pricing very junior and senior tranches or when computing index tranches (or index base correlation) sensitivities. Our numerical tests on realistic cases showed that the equivalent correlation provided by this new is pretty close to what is computed with common mapping functions

Diversification Potential of Structured Securities

Diversification has been a frequently stated benefit of structured securitizations. In the subprime crisis, however, CDOs (especially ABS CDOs) proved to be concentrations of risk. In this article, the author examines different diversification patterns of structured securities that were deemed beneficial by investors and finds that name diversification is largely ineffective and may even increase the risk of tranches. Similarly, factor or sector diversification in the pool may not have the anticipated effect. Positive effects are only achievable for senior tranches, and for mezzanine tranches, the risks may even increase. These results shed new light on the diversification potential of CDOs, which is important in terms of both risk management and valuation.

Systematic and Liquidity Risk in Subprime-Mortgage Backed Securities

The misevaluation of risk in securitized financial products is central to understanding the Financial Crisis of 2007-2008. This paper characterizes the evolution of factors affecting collateralized debt obligations (CDOs) based on subprime mortgages. A key feature of subprime-mortgage backed indices is that they are distinct in their vintage of issuance. Using a latent factor framework that incorporates this vintage effect, we show the increasing importance of a common factor on more senior tranches during the crisis. We examine this common factor and its relationship with spreads. We estimate the effects on the common factor of the financial crisis.

Pricing CDOs with State Dependent Stochastic Recovery Rates

Up to the 2007 crisis, research within bottom‐up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions.In this paper, we focus first on deterministic recovery rates in a factor copula framework. We use stochastic orders theory to assess the impact of a recovery markdown on CDOs and show that it leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models.We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or equivalently the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios that when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point.We also deal with implementation and numerical issues related to the pricing of CDOs within the stochastic recovery rate framework. Due to differences across names regarding the conditional (on the factor) losses given default, the standard recursion approach becomes problematic. We suggest approximating the conditional on the factor loss distributions, through expansions around some base distribution.Finally, we show that the independence and comonotonic cases provide some easy to compute bounds on expected losses of senior or equity tranches.

Re-REMICs: New and Improved

Most of the RMBS securities originally purchased with an AAA rating and thought to have little or no credit risk have either been downgraded or are likely to be downgraded and will eventually take credit losses. These instruments no longer fit the needs of regulated institutions or of total return money managers and are mandated to manage only highly rated assets. By providing more credit support to the senior tranche through a re-REMIC structure, properly enhanced AAA securities that better meet the needs of investors can be created. These securities are priced very attractively as alternative investment opportunities.

Pricing distressed CDOs with stochastic recovery

In this article, a framework for the joint modelling of default and recovery risk in a portfolio of credit risky assets is presented. The model especially accounts for the correlation of defaults on the one hand and correlation of default rates and recovery rates on the other hand. Nested Archimedean copulas are used to model different dependence structures. For the recovery rates a very flexible continuous distribution with bounded support is applied, which allows for an efficient sampling of the loss process. Due to the relaxation of the constant 40% recovery assumption and the negative correlation of default rates and recovery rates, the model is especially suited for distressed market situations and the pricing of super senior tranches. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. Applications to delta hedging as well as base correlations are presented.

Utility valuation of multi-name credit derivatives and application to CDOs

We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyse resulting yield spreads in multi-name credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyse the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

Lévy base correlation

AbstractIn this paper we investigate one‐factor models that extend the classical Gaussian copula model for pricing tranches of CDOs. We introduce Lévy base correlation and compare it to the classical Gaussian copula. The results of a historical study of both models on the iTraxx Europe Main dataset are presented. Our focus is on the base correlation surface and on the deltas of the tranches with respect to the index. We observe that the Lévy base correlation curve is much flatter than the corresponding Gaussian one. With respect to the deltas we conclude that the Lévy model produces larger deltas for the equity tranche and smaller deltas for the senior tranches. Copyright © 2009 Wilmott Magazine Ltd

Losses in Investment-Grade Tranches of Synthetic CDO's: A Large Deviations Analysis

Rare events are an important part of the financial world. For instance, investment-grade financial products by design should suffer losses only rarely. In many cases, this is accomplished by pooling a large number of assets and trancheing the losses. This often leads to a very complex system. We the theory of large deviations, a collection of tools for studying the origination and transformations of rare events, to address some of these issues in losses in senior tranches of synthetic collateralized debt obligations, which in some sense is an archetype of structured finance. Our calculations are fairly self-contained.

Pricing Distressed CDOs Under Stochastic Recovery

We present a framework for the joint modeling of default and recovery risk in a portfolio of credit risky assets, especially taking account for the correlation of defaults on the one hand and correlation of default rates and recovery rates on the other hand. We use nested Archimedean copulas to model different dependence structures and a very flexible, continuous recovery rate distribution with bounded support which allows for an efficient sampling of the loss process. Due to the relaxation of the constant 40% recovery assumption and the negative correlation of default rates and recovery rates, the model is especially suited for distressed market situations and the pricing of super senior tranches. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of our model.

A Top-Down Approach for MBS, ABS and CDO of ABS: A Consistent Way to Manage Prepayment, Default and Interest Rate Risks

We define a new approach to manage prepayment, default and interest rate risks simultaneously in some standard asset-backed securities structures. We propose a parsimonious top-down approach, by modeling directly the portfolio loss process and the amortization process. Both are correlated to interest rates. The methodology is specified for sequential- and pro-rata pay bonds (ABS, CMO, CDO of ABS), cash or synthetic. We prove analytical formulas to price all tranches, under and without the simplifying assumption that amortization occurs in the most senior tranche only. The model behavior is illustrated through the empirical analysis of an actual synthetic ABS trade.

Pricing Distressed CDOs with Base Correlation and Stochastic Recovery

In February and March 2008 it was temporarily not possible to calibrate the standard Gaussian Base correlation model to the complete set of CDX.IG and ITRAXX.IG CDO tranche quotes. For instance, in CDX.IG it failed for the 15%-30% senior tranche and hence the sucessive 30%-100% tranche. The reason is that the Gaussian Base correlation model was not able to generate enough probability for high portfolio losses, while preserving the calibration to mezzanine and equity tranches. We introduce a Gaussian Base correlation model with correlated stochastic recovery rates to overcome this problem. Moreover, our model can be used to price super senior tranches (e.g. 60%-100%), which have a fair spread of zero in a standard copula model with fixed recovery.

Recent Highlights from Total Securitization

An unprecedented number of collateralized debt obligations will hit their events-of-default triggers as a result of massive downgrades by Moody’s Investors Service. Over the next 12 months, as many as 20% of the 2006 and 2007 vintage structured finance CDOs could hit EOD, said David Yan, head of CDO research at Credit Suisse. Last Thursday, Moody’s downgraded $33.4 billion subprime first-lien residential mortgage-backed securities. Another $23.8 billion of the bonds were placed on review for possible downgrade. The downgrades rocked the market not only for the sheer notional value of the bonds affected, but also for the severity, with about 32% of the downgraded Baa bonds falling to Caa or below. Events of default can be triggered for a variety of reasons, including inadequate overcollateralization coverage, willful violation of a covenant, and interest shortfalls to the AAA investor. As a result of hitting the EOD, the controlling classholder—typically the super senior investor—will likely choose the acceleration of all the notes, which become immediately payable and due. Also, any reinvestment period would be terminated, making the deal static. Yan noted that how that plays out depends on the transaction’s covenants and liquidation waterfall, unique to each deal. Analysts at Derivative Fitch said the rating agency had already received an event of default notice on at least one structuredfinance CDO and “expects more deals to declare EODs as the underlying collateral continues to deteriorate.” In contrast with the large number of EOD notices expected now, only roughly 12 notices were received on 2000, 2001, and 2002 vintages, which suffered from the inclusion of such collateral as manufactured housing and franchise loans, Yan said. High-grade ABS CDOs will be particularly hard hit as their senior tranches have thinner subordination levels, about 20% versus 50% for mezzanine deals. At the same time, they have larger buckets for other CDOs: 25% compared with 10% for mezz deals. CDO squared will be affected even more severely. “It’s hard to see how any part of their portfolio could escape unscathed,” said one investor. As banks race to calculate how close their CDOs are to EOD, the question becomes how the controlling classholders will react. One investor noted that the controlling interest could choose to liquidate the portfolio quickly, which would leave them open to heavy mark-to-market losses. One broker dealer has reportedly disseminated a letter notifying investors that it may Recent Highlights from

Effect of Coverage Triggers on CDO Tranche Returns

Accurately estimating returns on CDO tranches is complicated, particularly when the structure of the CDO contains over-collateralization and interest-coverage triggers. Coverage triggers serve to divert cash flows from more junior tranches to retire principal of senior tranches under conditions of deteriorating collateral pool. We analyzed the effects of typical coverage triggers on distributions of expected tranche returns using Monte Carlo simulation. Results from simulated returns show that coverage triggers increase returns to senior tranche holders, but increase volatility of cash flows from CDOs during their reinvestment periods. Although triggers provide protection to senior holders at the expense of more junior investors, greater alignment of manager incentives with investors in all parts of a deal may serve to increase risk-adjusted returns on the collateral. <b>TOPICS:</b>CLOs, CDOs, and other structured credit, simulations

CDO Rating Methodology: Some Thoughts on Model Risk and its Implications

Rating collateralised debt obligations (CDOs), which are based on tranched pools of credit exposures, does not only require attributing a probability of default to each obligor within the portfolio. It also involves assumptions concerning recovery rates and correlated defaults of pool assets, thus combining credit assessments of individual collateral assets with estimates about default correlations and other modelling assumptions. In this paper, we explain one of the most well-known models for rating CDOs, the so-called binomial expansion technique (BET). Comparing this approach with an alternative methodology based on Monte Carlo simulation, we then highlight the potential importance of correlation assumptions for the ratings of senior CDO tranches and explore what differences in methodologies across rating agencies may mean for senior tranche rating outcomes. The remainder of the paper talks about potential implications of certain assumptions for ratings accuracy, that is the model risk taken by investors when acquiring CDO tranches, and whether and under what conditions methodological differences may generate incentives for issuers to strategically select rating agencies to get particular CDO structures rated.

Indifference prices of structured catastrophe (CAT) bonds

We present a method for pricing structured CAT bonds based on utility indifference pricing. The CAT bond considered here is issued in two distinct notes called tranches, specifically senior and junior tranches each with its own payment schedule. Our contributions to the literature of CAT bond pricing are two-fold. First, we apply indifference pricing to structured CAT bonds. We find a price for the senior tranche as a relative indifference price, that is, relative to the price of the junior tranche. Alternatively, one could take the approach that the senior tranche is priced first and the price of the junior tranche is relative to that. Second, instead of simply supposing that the “not-issue-a-CAT-bond” strategy of the reinsurer is to do nothing, we suppose that the reinsurer reduces its risk by reinsuring proportionally less claims. We assume that the reinsurance claims follow a (Poisson) jump–diffusion process.

An Empirical Investigation of an Intensity-Based Model for Pricing CDO Tranches

Using an extensive data set of 15,600 CDS and CDO tranche spreads I conduct an empirical analysis of a Duffie and Garleanu (2001) intensity-based model for correlated defaults. I examine the model with respect to model assumptions, pricing in both the cross section and time series dimension, and hedging ability. The model as- sumptions are found to be reasonable and the model prices and hedges the most risky tranches well. While the model does not capture the variability in senior spreads over time it matches the average spread of senior tranches.

Hybrid Assets in an ABS CDO

The term “hybrid” refers to CDO assets being comprised of both ABS credit default swaps (CDS) and asset-backed securities (ABS) cash bonds. This article reviews the advantages of the hybrid ABS CDO structure: increased access to collateral, more diversified portfolios, shorter collateral ramp-up periods, diminishment of available funds cap risk, flexibility to switch from cash to synthetic assets to take advantage of negative or positive basis, and cheap super-senior credit protection. The article then reviews four cash flow challenges faced by structurers of hybrid ABS CDOs. First, hybrid CDOs make CDS protection payments by drawing upon their reserve funds and super senior tranches. Second, during the reinvestment phase of a CDO, CDS amortization can be reinvested in new CDS or used to free up the reserve fund or the unfunded super-senior tranche to allow the purchase of cash ABS. During the CDO9s amortization period, ABCDS amortization can be used to amortize the unfunded super-senior tranche or free up the reserve fund to amortize the CDO9s cash liabilities. Third, cash asset amortization is first available for unpaid expenses and deferred interest on CDO liabilities. During the reinvestment period, if cash amortization is not used to purchase new cash assets, it must first be used to pay down the funded super-senior tranche and then to increase the reserve fund. Either use allows the CDO to sell additional CDS protection. Finally, in trading CDS, the CDO manager has to choose among termination, assignment, and offset. Offset is more commonly available, but carries with it operational burdens and prepayment or extension risk. <b>TOPICS:</b>Asset-backed securities, credit default swaps, credit risk management

Evaluation of tranche in securitization and long-range Ising model

This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J / N and the external field H as a model for homogeneous credit portfolio of assets with default probability P d and default correlation ρ d . Based on the discussion on the ( J , H ) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for P d , ρ d and the normalization factor Z in terms of the model parameters N and J , H . The effect of the default correlation ρ d on the probabilities P ( N d , ρ d ) for N d defaults and on the cumulative distribution function D ( i , ρ d ) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρ d and that of the senior tranche increases linearly, which are important in their pricing and ratings.

The Credit Risk Transfer Market and Stability Implications for U.K. Financial Institutions

The increasing ability to trade credit risk in financial markets has facilitated its dispersion across the financial and other sectors. However, specific risks attached to credit risk transfer (CRT) instruments in a market with still-limited liquidity means that its rapid expansion may actually pose problems for financial sector stability in the event of a major negative shock to credit markets. This paper attempts to quantify the exposure of major U.K. financial groups to credit derivatives, by applying a vector autoregression (VAR) model to publicly available market prices. Our results indicate that use of credit derivatives does not pose a substantial threat to financial sector stability in the United Kingdom. Exposures across major financial institutions appear sufficiently diversified to limit the impact of any shock to the market, while major insurance companies are largely exposed to the safer senior tranches.