Banachewicz, Konrad , André Lucas, "Quantile Forecasting for Credit Risk Management Using Possibly Mis-specified Hidden Markov Models", Journal of Forecasting, Vol. 27, No. 7, (July 2008), pp. 566-586.
Abstract: Recent models for credit risk management make use of hidden Markov models (HMMs). HMMs are used to forecast quantiles of corporate default rates. Little research has been done on the quality of such forecasts if the underlying HMM is potentially misspecified. In this paper, we focus on misspecification in the dynamics and dimension of the HMM. We consider both discrete- and continuous-state HMMs. The differences are substantial. Underestimating the number of discrete states has an economically significant impact on forecast quality. Generally speaking, discrete models underestimate the high-quantile default rate forecasts. Continuous-state HMMs, however, vastly overestimate high quantiles if the true HMM has a discrete state space. In the reverse setting the biases are much smaller, though still substantial in economic terms. We illustrate the empirical differences using US default data.
Keywords: defaults, Markov switching, misspecification, quantile forecast, expectation maximization, simulated maximum likelihood, importance sampling.