Statistics Seminar: Jennifer Chan -- Quantile regression for conditional autoregressive range model

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.