Forecasting Value-at-Risk with a duration-based POT method

Threshold methods, based on fitting a stochastic model to the excesses over a threshold, were developed under the acronym POT (peaks over threshold). To eliminate the tendency to clustering of violations, we propose a model-based approach within the POT framework that uses the durations between excesses as covariates. Based on this approach we suggest models for forecasting one-day-ahead Value-at-Risk. A simulation study was performed to validate the estimation procedure. Comparative studies with global stock market indices provide evidence that the proposed models can perform better than state-of-the art risk models and better than the widely used RiskMetrics model in terms of unconditional coverage, clustering of violations and capital requirements under the Basel II Accord.