Dec 24

Model risk in pricing a CDO

by David Harper, CFA, FRM, CIPM

FRM | CFA |

academicInsight

The experts at Kamakura Corporation published a fascinating study on collateralized debt obligation (CDO) valuation: "CDO Valuation: Fact and Fiction." One challenge in pricing a CDO is the large number of underlying exposures: the default correlation structure (i.e., among the underlying exposures) is perhaps the key input(s) into the model. Default correlations in CDOs are critical and counterintuitive; e.g., high default correlation hurts the senior tranche but helps the junior tranche.

The traditional way to value CDOs is to use Guassian copulas. Two model assumptions here can include: the use of a single-period model and a static correlation structure over time. This paper makes a strong case for why these two assumptions are deadly. Together, they arguably invalidate the model. Backed by an extensive multi-period Monte Carlo simulation, Robert A. Jarrow, Li Li, Mark Mesler, and Donald R. van Deventer argue that "the standard copula based CDO valuation model, and its standard simulation based implementation, has two serious deficiencies." These two deficiencies are:

  • A single-period model assumes default probabilities and correlations are constant (static) over the life of a CDO; e.g., a 5-year horizon is typical.
  • A typical (simplistic) correlation structure assumes all pairs of credits have identical default correlations

They demonstrate how these two defects generate CDO valuations that are "optimistic." Their alternative is a dynamic multi-period model "that allows both the default probabilities and correlations to vary with the business cycle."

What I especially find intriguing about their approach is that it links the default probability of each reference name (underlying exposure) to several macro-economic variables. So, their alternative includes two innovations: it is multi-period and it tries to adjust for business (economic cycles). They argue the following advantages:

  • This enables "one-month default probabilities (PDs) to vary across the  business cycle," and
  • This "induces business cycle variations in the default correlations as well.:

In short, their valuation model attempts to incorporate pro-cyclicality via both PDs and the correlation structure.

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