Volatility Proxies for Discrete Time Models

Discrete time volatility models typically employ a latent scale factor to represent volatility. High frequency data may be used to construct proxies for these scale factors. Examples are the intraday high-low range and the realized volatility. This paper develops a method for ranking and optimizing volatility proxies. It is possible to outperform the quadratic variation as a proxy for the discrete time scale factor. For the S&P 500 index data over the years 1988-2006 this is achieved by a proxy which puts, among other things, more weight on the highs than on the lows over intraday intervals.