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FRM Part II · FRM Exam Part II · Range of Practices and Issues in Economic Capital Frameworks

A bank aggregates market and credit risk using a Gaussian copula calibrated to a moderate correlation. A reviewer argues the approach may understate joint extreme losses. Which is the best reason?

The Gaussian copula exhibits no tail dependence, so it assigns too little probability to simultaneous extreme losses compared with copulas such as the t copula. Aggregated capital at high confidence levels may therefore be understated.

  1. AThe Gaussian copula has no tail dependence, so joint extreme events are assigned too little probability relative to heavy-tail-dependent copulas such as the t copulaCorrect
  2. BThe Gaussian copula assumes perfect correlation, which overstates capital
  3. CThe Gaussian copula cannot be applied to more than one risk type
  4. DThe Gaussian copula produces correlations above one in stress

Explanation

The Gaussian copula has zero asymptotic tail dependence, so for a given correlation it gives lower probability to simultaneous extreme losses than a t copula. Using a t copula would typically raise aggregated tail capital.

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