Modeling the Asymmetry of Stock Movements Using Price Ranges

It is shown in Chou (2005). Journal of Money, Credit and Banking, 37, 561–582that the range can be used as a measure of volatility and the conditional autoregressive range (CARR) model performs better than generalized auto regressive conditional heteroskedasticity (GARCH) in forecasting volatilities of S&P 500 stock index. In this paper, we allow separate dynamic structures for the upward and downward ranges of asset prices to account for asymmetric behaviors in the financial market. The types of asymmetry include the trending behavior, weekday seasonality, interaction of the first two conditional moments via leverage effects, risk premiums, and volatility feedbacks. The return of the open to the max of the period is used as a measure of the upward and the downward range is defined likewise. We use the quasi-maximum likelihood estimation (QMLE) for parameter estimation. Empirical results using S&P 500 daily and weekly frequencies provide consistent evidences supporting the asymmetry in the US stock market over the period 1962/01/01–2000/08/25. The asymmetric range model also provides sharper volatility forecasts than the symmetric range model.