Abstract: To calculate value-at-risk (VaR) for risk management, we derive parametric quantile functions. The general technique is to first build a mean regression model and then estimate families of conditional quantile functions based on the mean regression model. Instead, we propose to regress directly on the quantiles of a distribution and demonstrate the method through the conditional autoregressive range (CARR) model which has increased popularity recently. Two flexible distribution families: the generalized beta type two on positive support and the generalized-t on real support are adopted for demonstration. Then, the models are extended to model the volatility dynamic and compared in terms of goodness-of-fit. The models are implemented using the module fminsearch in Matlab under the classical likelihood approach and applied to analyse the intra-day high-low price ranges from the All Ordinaries index for the Australian stock market to obtain value-at-risk forecasts. VaR are forecast using the proposed models.