Approximations and control variates for pricing portfolio credit derivatives

Portfolio credit derivatives that depend on default correlation are increasingly widespread in the credit market. Valuing such products often entails Monte Carlo simulation. However, for large portfolios, plain Monte Carlo simulation can be slow. In this paper, we develop approximation methods for pricing collateralized debt obligation (CDO) tranches in the widely used factor copula approach. We also discuss using the approximations as control variates to improve the precision of Monte Carlo estimates. These approximation methods and control variate techniques could be applied to pricing other portfolio credit derivatives as well.