Measuring marginal risk contributions in credit portfolios

The Fourier Transform Monte Carlo (FTMC) method, a powerful algorithm for robust computation of marginal risk contributions and capital allocations for credit portfolios in the framework of mixture models, is presented. The method outperforms results obtained from simple Monte Carlo simulations which are flawed by high variances if expected values conditional on rare events are calculated. The FTMC method exploits the conditional independence property of the underlying latent variable model and, in addition, makes use of the Fast Fourier Transform technique for risk aggregation. Marginal risk contributions for expected shortfall, value at risk and capital at risk are presented for a synthetic but realistic credit portfolio.