Essays in portfolio credit risk

This thesis addresses several problems in credit risk. We first consider an estimation problem for a dynamic default model with discrete market observations. In the dynamic model, all the marginal defaults follow intensity based models, and default barriers are linked by a copula function; in this manner individual defaults are modeled separately from joint defaults. Our estimation procedure leverages off of this structure: in the first step we estimate the parameters of default rates; and in the second step we estimate the parameters of the copula function. The second problem we discuss in this thesis is the formulation of dynamic joint default models. In our models obligors may belong to different seniority classes and defaults can happen any time before maturity. We derive asymptotes for the probability of large default losses in a heterogeneous credit portfolio. To improve estimation accuracy of the probability of large losses in moderate sized portfolios, we develop importance sampling methods to estimate these probabilities by Monte Carlo simulation. Given the dynamic nature of the default models, the simulation of rare events relies on efficiently simulating the entire path of the modeling dynamics. This introduces further numerical errors and simulation "noise". To circumvent this issue we propose to simulate simpler events, related to upper and lower bounds on the tail probability. This leads to biased importance sampling estimators for the original tail probability. We then extend several concepts in standard (unbiased) importance sampling methods to the biased case. The final problem concerns managing portfolio credit risk for one of our proposed dynamic models. We formulate two portfolio selection problems and solve them using asymptotic analysis and importance sampling based simulation methods derived earlier.