Efficient estimation of unconditional capital by Monte Carlo simulation

We address the problem of determining the unconditional capital required by a credit portfolio using Monte Carlo simulation. By elaborating on a tractable analytical framework, we propose a new efficient simulation algorithm that overweights recession periods, which are the most important periods for determining the final capital figure, thereby improving its efficiency for a given number of simulations. We discuss the optimality and practical advantages of this algorithm. We also conduct an empirical analysis based on American charge-off data, which shows that the proposed algorithm achieves remarkable improvements in efficiency, without introducing any bias and at a negligible implementation cost.