A High-Low Model of Daily Stock Price Ranges

Abstract

This working paper was written by Yan-Leung Cheung (City University of Hong Kong), Yin-Wong Cheung (University of California, Santa Cruz) and Alan T. K. Wan (City University of Hong Kong).

We observe that daily highs and lows of stock prices do not diverge over time and, hence, adopt the cointegration concept and the related vector error correction model (VECM) to model the daily high, the daily low, and the associated daily range data. The in-sample results attest the importance of incorporating high-low interactions in modeling the range variable. In evaluating the out-of-sample forecast performance using both mean-squared forecast error and direction of change criteria, it is found that the VECM-based low and high forecasts offer some advantages over some alternative forecasts. The VECM-based range forecasts, on the other hand, do not always dominate - the forecast rankings depend on the choice of evaluation criterion and the variables being forecasted.

Keywords: Daily High, Daily Low, VECM Model, Forecast Performance, Implied Volatility

JEL Classification: C32, C53, G10