Forecasting Volatility Using Historical Data

Abstract

Applying modern option valuation theory requires the user to forecast the volatility of the underlying asset over the remaining life of the option, a formidable estimation problem for long maturity instruments. The standard statistical procedures using historical data are based on assumptions of stability, either constant variance, or constant parameters of the variance process, that are unlikely to hold over long periods. This paper examines the empirical performance of different historical variance estimators and of the GARCH (1,1) model for forecasting volatility in important financial markets over horizons up to five years. We find several surprising results: In general, historical volatility computed over many past periods provides the most accurate forecasts for both long and short horizons; root mean squared forecast errors are substantially lower for long term than for short term volatility forecasts; it is typically better to compute volatility around an assumed mean of zero than around the realized mean in the data sample, and the GARCH model tends to be less accurate and much harder to use than the simple historical volatility estimator for this application.