Comparison of Volatility Measures: a Risk Management Perspective

Volatility measurement has received a boost from the availability of ultra–high frequency data (UHFD) sampled at different frequencies which need to be complemented by appropriate methods to project volatility behavior. In this paper we take a risk management perspective and address the issue of forecasting Value–at–Risk (VaR) using different volatility measures: realized volatility, bipower realized volatility, two scales realized volatility, as well as the daily range. For the sample and assets chosen, volatility clustering occurs around a changing level in average volatility; other features such as persistence and shape appear to change with the UHFD sampling frequency. Building on the existing literature, we propose a novel modeling approach that captures the features of the series called P–Spline Multiplicative Error Model. Such an approach consists of a dynamic model with a flexible trend specification bonded with a penalized maximum likelihood estimation strategy that enhances forecasting ability. Results show that exploiting UHFD volatility measures, VaR predictive ability is improved upon relative to a baseline GARCH approach but the range is not outperformed and that there are relevant gains from modeling volatility trends and the nonnormality of the conditional return distribution.