medium · FRM Part 1 Quantitative Analysis

Which statement correctly characterizes the difference that matters for her tail-risk modeling?

1. The Gaussian copula has zero coefficient of upper and lower tail dependence for any ρ<1, while the t copula exhibits symmetric, strictly positive tail dependence that increases as the degrees of freedom fall, so only the t copula captures joint extreme co-movements at the calibrated ρ.
2. Both copulas have the same tail dependence because they share the same correlation ρ; the only real difference is that the t copula has fatter marginal tails, which is irrelevant once the two portfolios' marginal loss distributions are fitted and modeled separately from the dependence structure.
3. The Gaussian copula has higher tail dependence than the t copula at ρ=0.5 because the normal distribution concentrates so much probability mass tightly near the center of its joint density that it necessarily forces extreme outcomes to occur jointly there instead of independently across the two portfolios.
4. The t copula has positive upper tail dependence but exactly zero lower tail dependence at any degrees-of-freedom parameter, which makes it well suited for modeling joint upside co-movement but not for the joint default scenario she is actually most worried about here in her credit portfolios.

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