This paper addresses the risk analysis and market valuation of collateralized debt obligations (CDOs). We illustrate the effects of correlation and prioritization for the market valuation, diversity score, and risk of CDOs, in a simple jump-diffusion setting for correlated default intensities. ACDO isanasset-backed security whose underlying collater al is typicallya portfolio of bonds (corporate or sovereign) or bank loans.
ACDO 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. Some illustrative examples of prioritization are provided in Section 4.
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 re garding 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 in which the CDO tranches receive payments based essentially on the mark-to-market returns of the collateral pool, as determined in large part by the trading performance of the CDO manager. In this paper, we concentrate on cash-flow CDOs, avoiding an analysis of the trading behavior of CDO managers.
A generic example of the contractual relationships involved in a CDO is shown in Figure1, taken from Schorinand Weinreich[1998]. The collateral manager is charged with the selection and purchase of collateral assets for the SPV. The trustee of the CDO is responsible for monitoring the contractual provisions oft he 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.
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Risk and Valuation of Collateralized Debt Obligations
