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FRM Part II · FRM Exam Part II · Portfolio Credit Risk

A risk team calibrates a Gaussian copula to a CDO tranche and finds that the implied correlation differs between the equity tranche and the senior tranche (a correlation skew). What is the most appropriate interpretation?

A correlation skew means the single-parameter Gaussian copula cannot reproduce all tranche prices with one correlation. It signals model misspecification, analogous to the volatility smile in option pricing, rather than arbitrage or evidence for any particular alternative model.

  1. AThe single-correlation Gaussian copula does not fully capture market pricing of tranche risk, so one correlation cannot fit all tranchesCorrect
  2. BMarket prices are arbitrage-free only if all tranche implied correlations are identical
  3. CThe correlation skew shows that the underlying default probabilities are deterministic
  4. DThe skew proves that the t copula must price all tranches perfectly

Explanation

Different implied correlations across tranches show the flat-correlation Gaussian copula is a misspecified model for market prices, much as a volatility smile does for Black-Scholes. It does not imply arbitrage, deterministic defaults, or that any alternative copula fits perfectly.

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