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

A credit portfolio manager notes that the Gaussian copula implies that joint defaults become nearly independent in the extreme tail even when asset correlation is high. Which property of the Gaussian copula does this describe, and what is its main practical implication for senior CDO tranche valuation?

The Gaussian copula has zero tail dependence, meaning extreme joint defaults behave nearly independently regardless of the correlation parameter. As a result it can understate the probability of clustered extreme defaults and therefore underestimate the risk and fair spread of senior tranches in crises.

  1. ATail dependence is zero, so the model can understate the probability of clustered extreme defaults and underprice senior tranche riskCorrect
  2. BTail dependence is one, so the model overstates clustered defaults and overprices senior tranche risk
  3. CThe copula lacks a correlation parameter, so it cannot be calibrated to market prices
  4. DThe copula forces default times to be deterministic, so recovery rates become the only source of uncertainty

Explanation

The Gaussian copula has no (asymptotic) tail dependence, so in extreme scenarios defaults tend toward independence. This tends to understate the likelihood of widespread simultaneous defaults, which matters most for senior tranches.

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