Ranking and Combining Volatility Proxies for Garch and Stochastic Volatility Models

Daily volatility proxies based on intraday data, such as the high-low range and the realized volatility, are important to the specification of discrete time volatility models, and to the quality of their parameter estimation. The main result of this paper is a simple procedure for combining such proxies into a single, highly efficient volatility proxy. The approach is novel in optimizing proxies in relation to the scale factor (the volatility) in discrete time models, rather than optimizing proxies as estimators of the quadratic variation. For the S&P 500 index tick data over the years 1988-2006 the procedure yields a proxy which puts, among other things, more weight on the sum of the highs than on the sum of the lows over ten-minute intervals. The empirical analysis indicates that this finite-grid optimized proxy outperforms the standard five-minute realized volatility by at least 40%, and the limiting case of the square root of the quadratic variation by 25%.