FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches
A bank holds a mezzanine CDO tranche and observes that, after a market shock, the implied correlation for the equity tranche (compound correlation) differs from that of the mezzanine tranche on the same portfolio. What is the most appropriate interpretation?
Different implied correlations across tranches indicate a correlation smile, showing the single-correlation Gaussian copula does not fit observed tranche prices. A correctly specified model would imply one correlation for every tranche, so the differences point to model misspecification rather than arbitrage or recovery assumptions.
- AThe Gaussian copula is well specified because correlation should differ by tranche
- BThe market is revealing a correlation smile, indicating the Gaussian copula with a single constant correlation does not fit tranche pricesCorrect
- CThe tranches must be mispriced and an arbitrage exists in default probabilities
- DImplied correlation differences arise only from differing recovery rates across tranches
Explanation
If the Gaussian copula with a flat correlation held, all tranches would imply the same correlation. Different implied correlations across attachment points form a correlation smile/skew, evidence of model misspecification. It does not by itself prove arbitrage, and recovery rates are not the sole explanation.
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