Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intra-day Range

Abstract

Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We pro-pose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 fnancial crisis, and evaluate how the crisis afects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more eficiently than other models, across the series considered, which should be useful for financial practitioners.