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Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models by Roberto Torresetti, Andrea Pallavicini, Damiano Brigo

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7
Application to More Recent Data and the Crisis
In this chapter we check whether the critical features we discussed about implied correlation and the subsequent elements coming from more advanced models are still present in-crisis, after mid-2007. We will observe that the features are still present and often amplified in the market after the beginning of the crisis.

7.1 COMPOUND CORRELATION IN-CRISIS

We begin by extending the sample of the compound correlation invertibility analysis to see if the non-invertibility arose again during the market turmoil in 2007-2009 (see Figures 7.1 to 7.4 on pages 88 to 91). As before, we resort to the homogeneous pool model.
In Figures 7.2 and 7.4 we notice how, since the credit crunch began in Summer 2007, the problematic tranches changed. In fact, the non-invertibility affected
1. For the DJ-iTraxx, 10-year 12-22% tranche (see Figure 7.2);
2. For the CDX pool the 10-year 10-15% and more marginally the 10-year 15-30% tranche (see Figure 7.4).
Another relevant issue, besides the non-invertibility of compound correlation, is its non-uniqueness when invertible. We have seen in Figure 3.1 that on 3 August 2005 for some tranches the map between correlation and theoretical tranche spread is not monotonic. In particular, we have seen how this resulted for the DJ-iTraxx 10-year 6-9% and the DJ-iTraxx 10-year 9-12% tranches.
Figure 7.1 DJ-iTraxx 5-year compound correlation invertibility. Market spread (black line) versus minimum and maximum tranche ...

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