This study evaluates the performance of nine alternative models for predicting stock price volatility using daily New Zealand data. The competing models contain both simple models such as the random walk and smoothing models and complex models such as ARCH-type models and a stochastic volatility model. Four different measures are used to evaluate the forecasting accuracy. The main results are the following: (1) the stochastic volatility model provides the best performance among all the candidates; (2) ARCH-type models can perform well or badly depending on the form chosen: the performance of the GARCH(3,2) model, the best model within the ARCH family, is sensitive to the choice of assessment measures; and (3) the regression and exponentially weighted moving average models do not perform well according to any assessment measure, in contrast to the results found in various markets.