Modelling and Forecasting Stock Volatility and Return : A New Approach Based on Quantile Rogers-Satchell Volatility Measure With Asymmetric Bilinear CARR Model

Rogers-Satchell (RS) measure is an efficient volatility measure. This paper proposes quantile RS (QRS) measure to ensure robustness and correct the downward bias of RS measure with an additive term. Moreover scaling factors are provided for different interquantile ranges to ensure unbiasedness. Simulation studies confirm the efficiency of QRS measure relative to the intraday (open-to-close) squared returns and RS measures in the presence of intraday extreme prices. To smooth out the noises, QRS measures are fitted to the conditional autoregressive range (CARR) model with different asymmetric mean functions and error distributions. These fitted volatilities are then incorporated into return models to capture the heteroskedasticity of returns. Different value-at-risk (VaR) and conditional VaR return forecasts are provided and tested. Results based on Standard and Poor 500 and Dow Jones Industrial Average indices show that volatility estimates using QRS measures, asymmetric bilinear mean function and generalised beta type II distribution provide the best in-sample model-fit and out-of-sample forecast. For return models, the constant mean structure with Student-t errors and QRS volatility estimates provides the best in-sample fit. Different performance measures including Kupiec test for VaRs based on the best return model are evaluated to confirm the accuracy of the VaR forecasts