Time Series Volatility Forecasts for Option Valuation and Risk Management

Abstract

Option pricing models and longer-term value-at-risk models typically require volatility forecasts over horizons considerably longer than the data frequency. These are generally generated from short-horizon forecasts by successive forward substitution. We document deficiencies with the resulting long-horizon volatility predictions generated by GARCH type models, such as GARCH(1,1), EGARCH, and GJR. One, since volatility forecasts for forward periods are functions of forecast volatility for the next period, this recursive procedure keeps the relative weights of recent and older observations the same whether forecasting volatility in the near or distant future. In contrast, we find that older observations are relatively more important in forecasting at long horizons, e.g., more important in forecasting volatility next month than in forecasting volatility tomorrow. Two, forecasts of the return standard deviation - the most appropriate volatility measure for option valuation and value-at-risk models - are strongly positively biased. Three, GARCH(1,1) and GJR forecasts are especially biased following high volatility days. We find that the ARLS model of Ederington and Guan corrects these three deficiencies and generally forecasts better out-of-sample than GARCH, EGARCH, AGARCH and the GJR models across a wide variety of markets and forecast horizons.

Keywords: GARCH, EGARCH, volatility, options

JEL Classification: G13, C22, C53