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FRM Part II · FRM Exam Part II · Structured Credit Risk

A bank calibrates a homogeneous one-factor Gaussian copula to a 100-name portfolio and finds that implied correlations differ across tranches of the same index (equity higher/lower than mezzanine) when fit to market spreads. A senior risk officer asks what this correlation skew indicates. Which interpretation is most appropriate?

The correlation skew shows the flat-correlation Gaussian copula is misspecified. If it were right, one correlation would price every tranche of the same portfolio. Implied correlation is therefore a quoting convention, analogous to implied volatility, not a true common asset correlation, since tranches share identical underlying names.

  1. AThe single flat-correlation Gaussian copula is mis-specified for the market, so the implied correlation is a quoting convention rather than a true common asset correlationCorrect
  2. BThe market has confirmed that true asset correlation differs by seniority of the tranche
  3. CThe skew proves that default probabilities are constant over time
  4. DThe skew arises only from differences in recovery rate assumptions and disappears under standard recovery

Explanation

If the model were correct, one correlation would reprice all tranches. Differing implied correlations (the correlation smile/skew) show model misspecification, like the Black-Scholes implied volatility smile, so implied correlation is a quoting device. Base correlation is a related convention. Asset correlation cannot differ by tranche since tranches share the same underlying portfolio.

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