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What methods can be used to map the correlation skew of a credit index on a bespoke CDO portfolio?

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Find the most similar (in terms of credit risk and industry) quoted index tranches you can. Then map its base correlation skew over to your bespoke portfolio, preserving expected loss (EL) levels.

The basic formula is \begin{equation} c_\text{bespoke}(z) = c_\text{index}\left( z \frac{EL_\text{index}}{EL_\text{bespoke}} \right) \end{equation} though sometimes a scale factor $f$ is included like this \begin{equation} c_\text{bespoke}(z) = c_\text{index}\left( z \left( \frac{EL_\text{index}}{EL_\text{bespoke}} \right)^f \right) \end{equation}

The main flaw here is that the dispersion of your portfolio may differ from that of the index. Try to keep that difference to a minimum.

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    $\begingroup$ What if z (EL_index / EL_bespoke)^f > 1? $\endgroup$ – quant_dev Feb 14 '11 at 17:55
  • $\begingroup$ Typically no one really needs to price those super-senior tranches. I suppose that I would just extrapolate my base correlation curve with a constant. The copula model is merely the least bad of a dismal set of choices. $\endgroup$ – Brian B Feb 14 '11 at 18:19
  • $\begingroup$ I do. Wouldn't using a risk measure mapping work better in this case? $\endgroup$ – quant_dev Feb 14 '11 at 19:57
  • $\begingroup$ What do you mean by "risk measure mapping"? I am not familiar with the term. $\endgroup$ – Brian B Feb 15 '11 at 14:16
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    $\begingroup$ If you're up in the senior tranches I can see how TLP/RMM would be attractive (I totally forgot about that mapping method). I hate the copula model(s) up there but if the portfolio has already burned through some lower tranches then it is pretty sensible. $\endgroup$ – Brian B Feb 22 '11 at 18:54

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