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

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 propose 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 financial crisis, and evaluate how the crisis affects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices and two exchange rates????. We examine violation rates, back-testing criteria, market risk charges and quantile loss function to measure the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more efficiently than other models, which should be useful for financial practitioners.

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