Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range

Some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models are proposed that incorporate intra-day price ranges. Model estimation is performed using a Bayesian approach via the link with the Skewed–Laplace distribution. The performances of a range of risk models during the 2008–09 financial crisis are examined, including an evaluation of the way in which the crisis affected the performance of VaR forecasting. An empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices and two exchange rate series. Standard back-testing criteria are used to measure and assess the forecast performances of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more effectively and more accurately than other models, across the series considered.