A conditional independence approach for portfolio risk evaluation

ABSTRACT This paper proposes a portfolio risk evaluation method that assumes conditional independence. We consider some latent variables which determine the conditional distribution of the future price or the potential loss of a portfolio under the assumption of conditional independence, which means that, given the latent variables, default times are independent. The unconditional distribution is then given as the expectation of the conditional distribution. Whereas Martin, Thompson and Browne (2001a) define latent variables to be discrete, in our method the variables can also be continuous and are generated using Monte Carlo simulation. Since we use both simulation and analytical approximated formulas based on the saddlepoint method, we refer to our method as “hybrid”. Some numerical examples show that the hybrid method gives a more accurate distribution using less calculation time than the simulation, and the risk contributions to VAR and CVAR obtained by our method seem to be much more reliable than those obtained by simulation.