Mapping Credit Index Base Correlation Skew to a Bespoke CDO

Summary

The document presents a method for estimating the base correlation skew of a bespoke collateralized debt obligation portfolio when directly quoted market data are limited. It recommends finding quoted index tranches that resemble the bespoke portfolio in credit risk and industry composition, then transferring the index skew while matching expected loss levels.

The mapping rescales the bespoke portfolio’s attachment point by the ratio of expected losses for the index and bespoke portfolio before reading the corresponding index correlation. A variant raises that expected-loss ratio to a scale factor, allowing the mapping to be adjusted. The key caveat is portfolio dispersion: if the bespoke names have materially different risk dispersion from the index constituents, the transferred skew may be unreliable. The answer offers a practical approximation rather than validation against observed bespoke prices, and it supplies no procedure for selecting the scale factor.

Key ideas

• Use quoted index tranches similar in credit risk and industry to the bespoke portfolio.
• Transfer the index base correlation skew after adjusting for the portfolios’ expected loss levels.
• A scale factor can modify the expected-loss ratio used in the mapping.
• Differences in portfolio dispersion can undermine the approximation.

Tags

# Correlation skew mapping


# Correlation skew mapping












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

## Answer by Brian B (score 6, accepted)

https://quant.stackexchange.com/a/504

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.