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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas

A bank uses a Gaussian copula to model joint defaults across a loan portfolio. After a crisis, it is criticised because the model understated the frequency of simultaneous defaults. Which feature of the Gaussian copula best explains this criticism?

The Gaussian copula has no tail dependence, so it underestimates simultaneous extreme events such as joint defaults in a crisis. It can still be paired with any marginals and does not assume independence, but its joint tail probabilities decay too quickly.

  1. AIt has no tail dependence, so joint extreme events are underestimatedCorrect
  2. BIt cannot be combined with non-normal marginals
  3. CIt has upper tail dependence only
  4. DIt requires all marginals to be identical
  5. It assumes the defaults are independent

Explanation

The Gaussian copula has zero coefficient of tail dependence for correlation below 1, so the probability of joint extremes falls quickly. It can be used with any marginals and does not assume independence. Hence joint defaults in a crisis are understated.

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