Financial institutions and regulators usually measure credit risk only over a one-year time horizon. Hence, current statistical models can generate closed-form expressions for the one-year loss distribution. Losses over longer horizons are considered using scenario analysis or Monte Carlo simulation. This paper proposes a simple multi-period credit risk model and uses Taylor expansion approximations to estimate the multi-period loss distribution. In this paper we extend the currently available second-order Taylor expansion approximations to credit risk with a third-order term and we use this new approximation to obtain the loss distribution in the multi-period framework. Our results show that the approximation is more accurate under recessions or for portfolios with high probability of default. We also show that, in general, the effect of this third-order adjustment is quite small.

This paper quantifies the credit risk loss distribution of the Spanish financial system by introducing a general Monte Carlo importance sampling (IS) approach. We start obtaining all the required information for the standard credit risk model. Then we quantify the loss distribution under the standard IS method and allocate the total risk over the different institutions in the Spanish financial system. We extend the current IS framework to deal with more general assumptions like random recoveries and market valuation. We also study the variability of the risk measures over the business cycle and the possible variability due to the model parameters uncertainty. Our results show that this approach can be very useful for banking supervisors from a macroprudential point of view and that the risk allocation can vary considerably depending on the valuation model under analysis.