Using auto-regressive logit models to forecast the exceedance probability for financial risk management

Abstract

We present new auto-regressive logit models for forecasting the probability of a time series of financial asset returns exceeding a threshold. The models can be estimated by maximizing a Bernoulli likelihood. Alternatively, to account for the extent to which an observation does or does not exceed the threshold, we propose that the likelihood is based on the asymmetric Laplace distribution, which has been found to be useful for quantile estimation. We incorporate the exceedance probability forecasts within a new time varying extreme value approach to value at risk and expected shortfall estimation. We provide an empirical illustration using daily stock index data.