hard · FRM Part 1 Quantitative Analysis
An institutional credit portfolio consists of two idiosyncratic exposures, each with a 1-year marginal probability of default (PD) of PD_A = PD_B = 0.05.
If a risk manager utilizes a Gaussian copula with a correlation parameter ρ > 0 to model joint default, which statement correctly describes the relationship between the joint default probability P(D_A cap D_B) and the case of statistical independence?
- The joint default probability P(D_A cap D_B) will be strictly greater than 0.0025.
- The joint default probability P(D_A cap D_B) remains exactly 0.0025 because copulas do not alter marginal distributions.
- The joint default probability P(D_A cap D_B) will be less than 0.0025 due to the diversification benefit inherent in Gaussian modeling.
- The joint default probability P(D_A cap D_B) will equal 0.05 × ρ.
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