An approximate multi-period Vasicek credit risk model

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.