Volatility Forecasts for Option Valuations

Abstract

We document several problems with GARCH type model predictions over the multi-day horizons common to option valuations and value-at-risk models. One, GARCH model forecasts of the return standard deviation - the most common volatility measure and the most appropriate for option valuation and value-at-risk models - are positively biased. Two, the bias is especially severe following high volatility days. Three, in forecasting volatility over longer horizons, the GARCH model puts too little weight on older observations relative to the more recent observations. That is older observations are more important in forecasting volatility next month than in forecasting volatility tomorrow while the GARCH procedure treats them equally at both horizons. We present a simple unbiased regression estimator of the standard deviation of returns which avoids these problems. We find it forecasts better out-of-sample than GARCH, EGARCH, and historical volatility across a wide variety of markets and forecast horizons.