A collateralized debt obligations CDO is an asset-backed security whose underlying collateral is typically a portfolio of bonds (corporate or sovereign) or bank loans. A CDO cash flow structure allocates interest income and principal repayments from a collateral pool of different debt instruments to a prioritized collection of CDO securities, which we shall call tranches. While there are many variations, a standard prioritization scheme is simple subordination: Senior CDO notes are paid before mezzanine and lower-subordinated notes are paid, with any residual cash flow paid to an equity piece.
A cash flow CDO is one for which the collateral portfolio is not subjected to active trading by the CDO manager, implying that the uncertainty regarding interest and principal payments to the CDO tranches is determined mainly by the number and timing of defaults of the collateral securities. A market value CDO is one for which the CDO tranches receive payments based essentially on the mark-to-market returns of the collateral pool, which depends on the trading performance of the CDO asset manager.
A generic example of the contractual relationships involved in a CDO is shown in above picture. The collateral manager is charged with the selection and purchase of collateral assets for the special purpose vehicle (SPV). The trustee of the CDO is responsible for monitoring the contractual provisions of the CDO. Our analysis assumes perfect adherence to these contractual provisions. The main issue that we address is the impact of the joint distribution of default risk of the underlying collateral securities on the risk and valuation of the CDO tranches.We are also interested in the efficacy of alternative computational methods and the role of diversity scores, a measure of the risk of the CDO collateral pool that has been used for CDO risk analysis by rating agencies.
We will see that default-time correlation has a significant impact on the market values of individual tranches. The priority of the senior tranche, by which it is effectively “short a call option” on the performance of the underlying collateral pool, causes its market value to decrease with risk-neutral default-time correlation. The value of the equity piece, which resembles a call option, increases with correlation. However, there is no clear effect of optionality for the valuation of intermediate tranches. With sufficient over-collateralization, the option “written” (to the lower tranches) dominates, but it is the other way around for sufficiently low levels of over-collateralization. Market spreads, at least for conventional mezzanine and senior tranches, are not especially sensitive to the lumpiness of information arrival regarding credit quality. For example, for our jump-diffusion model of default intensity, replacing the contribution of diffusion with jump risks (of various types), holding constant the degree of covariance of risk-neutral default intensities and the term structure of credit spreads, generates relatively small changes in pricing. Regarding alternative computational methods, we show that if (risk-neutral) diversity scores can be evaluated accurately, which is computationally simple in the framework we propose, these scores can be used to obtain good approximate market valuations for reasonably well-collateralized tranches. Currently the weakest link in the chain of CDO analysis is the limited availability of empirical data bearing on the correlation of default risk.
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