Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data

Volatility of asset prices in financial market is not directly observable. Return-based models have been proposed to estimate the volatility using daily closing prices. Recently, many new range-based volatility measures were proposed to estimate the financial volatility. This paper proposes quantile Parkinson (QPK) measure to estimate daily volatility and to show how it can robustify the Parkinson (PK) measure in the presence of intraday extreme returns. Results from extensive simulation studies show that the QPK measure is more efficient than intraday (open-to-close) squared returns and PK measures in the presence of intraday extreme returns. To demonstrate the applicability of QPK measure, we analyse the daily Standard and Poor 500 index by fitting the QPK measure to the conditional autoregressive range (CARR) models. Results show that choosing a suitable interquantile level width for the QPK measure will reduce its variance and hence improve its efficiency. In addition, the QPK measure using asymmetric CARR model gives the best in-sample model fit based on Akaike information criterion and provides the best out-of-sample forecast based on root mean squared forecast error and other measures. Mincer Zarnowitz test is carried out to confirm the unbiasedness of the forecasted volatility. Different levels of value-at-risk and conditional value-at-risk forecasts are also provided and tested.