Value at Risk (VaR) is the metric adopted by the Basel Accords for banking industry internal control and regulatory reporting. This has focused attention on the measuring, estimating and forecasting of lower tail risk. Engle and Manganelli (2004) developed the conditional autoregressive value at risk (CAViaR) model using quantile regression to calculate VaR. In this article we apply their model to Australian stock market indices and a sample of stocks, and test the efficacy of four different specifications of the model in a set of in-sample and out-of-sample tests. We also contrast the results with those obtained from a Generalized Autoregressive Conditional Heteroskedastic (GARCH(1,1)) model, the RiskMetrics™ model (Morgan, 1996) and an Asymmetric Power Autoregressive Conditional Heteroskedastic (APARCH) model.
- quantile regression