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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

In 2005, an analyst computes implied correlations for standard index tranches and finds that the equity tranche implies a correlation of 15% while the mezzanine tranche implies a correlation of 5% for the same index under a Gaussian copula. Which conclusion is most appropriate?

The Gaussian copula with one flat correlation is inconsistent with market tranche prices. Different implied correlations across tranches create a correlation smile, much like the volatility smile, showing the model is misspecified rather than proving arbitrage or independence.

  1. AThe market is arbitrage-free because each tranche has its own correlation
  2. BThe Gaussian copula with a single flat correlation is inconsistent with observed tranche prices, showing a correlation smileCorrect
  3. CThe index must have mispriced default probabilities rather than correlation
  4. DThe implied correlation differences prove that defaults are independent

Explanation

If a single-correlation Gaussian copula were correct, all tranches would imply the same correlation. Different implied values across tranches form a correlation smile or skew, analogous to the volatility smile, indicating model misspecification. It does not prove independence or an arbitrage.

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