A key practical difficulty in credit risk modeling is that default correlations are very difficult to estimate empirically because defaults are rare events. Thus, statement (a) is true.

Regarding the other options: (b) is false because the ULC approximation for a large, uniform portfolio is $ULC_i \approx UL_i \times \sqrt{\rho}$, so for $\rho = 0.160$, the multiplier is $\sqrt{0.160} = 0.40$ (or 40%), not 16.0%. (c) is false because the number of pairwise correlations required is calculated as $n(n-1)/2 = 100 \times 99 / 2 = 4,950$, not $100!$. (d) is false because banks often rely heavily on numerical procedures (like Monte Carlo simulation) to handle the complexities and nonlinearities of actual credit portfolios, whereas analytical models have strict, often unrealistic assumptions.