CDO Valuation and Cash Flow Waterfall Models

This article studies the problem of default correlation. It introduces a random variable called “time-until-default” to denote the survival time of each defaultable entity or financial instrument, and defines the default correlation between two credit risks as the correlation coefficient between their survival times. The author explains why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. He shows that the current approach to default correlation through asset correlation is equivalent to using a normal copula function. Numerical examples illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

/pdf/on-default-correlation-a-copula-function-approach-3wexvt5evk.pdf

On Default Correlation: A Copula Function Approach

Synthetic collateralized debt obligations, or synthetic CDOs, are popular vehicles for trading the credit risk of a portfolio of assets. Following a brief summary of the development of the synthetic CDO market, I draw on recent innovations in modeling to present a pricing model for CDO tranches that does not require Monte Carlo simulation. I use the model to analyze the risk characteristics of the tranches of synthetic CDOs. The analysis shows that although the more junior CDO tranches - equity and mezzanine tranches - typically contain a small fraction of the notional amount of the CDO's reference portfolio, they bear a majority of the credit risk. One implication is that credit risk disclosures relying on notional amounts are especially inadequate for firms that invest in CDOs. I show how the equity and mezzanine tranches can be viewed as leveraged exposures to the underlying credit risk of the CDO's reference portfolio. Even though mezzanine tranches are typically rated investment-grade, the leverage they possess implies their risk (and expected return) can be many times that of an investment-grade corporate bond. The paper goes on to show how CDO tranches and other innovative credit products, such as single-tranche CDOs and first-to-default basket swaps, are sensitive to the correlation of defaults among the credits in the reference portfolio. Differences of opinion among market participants as to the correct default correlation can create trading opportunities. Finally, the paper shows how the dependence of CDO tranches on default correlation can also be characterized and measured as an exposure to the business cycle, or as business cycle risk. A mezzanine tranche, in particular, is highly sensitive to business cycle risk.

/pdf/understanding-the-risk-of-synthetic-cdos-2kg1d3pbue.pdf

CDO Valuation and Cash Flow Waterfall Models

References

On Default Correlation: A Copula Function Approach

Understanding the Risk of Synthetic CDOs

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