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.