Portfolio credit risk analysis involving CDO tranches

Credit risk analysis for portfolios containing CDO tranches is a challenging task for risk managers. We propose here a basis function approach for CDO tranche valuation and portfolio risk analysis at horizon, based on a multi-step Monte Carlo simulation model. The idea is to approximate the expected value of the tranche at horizon by a linear combination of basis functions, which are chosen to best characterize the current state of the associated CDO. It can be generalized for portfolio risk analysis involving any complex financial instruments.