hard · Frm Part 2 Market Risk

A portfolio of two corporate bonds has a 1-year default probability of PD_1 = PD_2 = 2%. The risk manager compares a Gaussian copula and a Student-t copula (with ν = 4 degrees of freedom), both calibrated to the same asset correlation of ρ = 0.25.

Which model will produce a higher joint default probability, and why?

  1. Both will produce identical joint default probabilities because the marginal PDs and correlation are matched.
  2. The Student-t copula, because it has fewer degrees of freedom than the Gaussian.
  3. The Gaussian copula, because the asset correlation is positive.
  4. The Student-t copula, because it exhibits tail dependence.

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