Forward Equations for Portfolio Credit Derivatives

Abstract

We introduce an alternative approach for computing the values of CDO tranche spreads in reduced-form models for portfolio credit derivatives ("top-down" models), which allows for efficient computations and can be used as an ingredient of an efficient calibration algorithm. Our approach is based on the solution of a system of ordinary differential equations, which is the analogue for portfolio credit derivatives of Dupire's famous equation for call option prices. It allows to efficiently price CDOs and other portfolio credit derivatives without Monte Carlo simulation.

Keywords: credit risk, portfolio credit derivatives, CDO, derivative pricing, tranche

JEL Classification: G13,C14, C63