We derive explicit sharp bounds on the distribution of the number of defaults from a pool of obligors with common probability of default and default correlation. These bounds are extremely wide, implying that default probabilities and default correlations only very loosely determine...

We discuss the general optimization problem of choosing a copula with minimum entropy relative to a specified copula and a computationally intensive procedure to solve its dual. These techniques are applied to constructing an empirical copula for CDO tranche pricing. The empirical copula is...