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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