FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches
A quant calibrates a Gaussian copula to a CDO and finds that the implied correlation needed to match the equity tranche differs from that needed for the mezzanine tranche. What is this phenomenon called, and what does it indicate?
This is a correlation smile. Needing different implied correlations for different tranches shows that the Gaussian copula with a single constant correlation cannot reproduce observed tranche prices consistently, indicating model misspecification.
- ACorrelation smile, indicating the model's single-correlation assumption is inconsistent with market pricesCorrect
- BVolatility skew, indicating equity options are mispriced
- CBase correlation floor, indicating correlations cannot be negative
- DCopula convergence, indicating the model is well calibrated
Explanation
Different implied (compound) correlations across tranches form a correlation smile, showing the Gaussian copula with one flat correlation does not fit market tranche prices. It is not a volatility concept, and it signals poor fit rather than good calibration.
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