Implied GARCH Volatility Forecasting
25 Pages Posted: 19 Feb 2002
Date Written: December 2001
This paper empirically investigates a method to quantify volatility using the information content of index options. We derive the parameters of a GARCH option pricing model from the term structure of the observed market smile of DAX 30 index. We find the EGARCH option pricing model (Duan, 1995) performs well in determining the shape of the volatility smile for different maturities in the period of January 2000 to August 2001. Based on the implied EGARCH methodology we use the information in option prices to derive a theoretically sound 'new' measure for local volatility and analyze how well it explains and forecasts actual realized volatility. The daily realized volatility measure is constructed with 5-minute interval transaction prices in the DAX 30 future. The local volatility measure explains a large part of realized volatility and performs considerably better in one day ahead volatility forecasting than conventional time-series models.
Keywords: Implied volatility, GARCH, index options, forecasting
JEL Classification: C.22, C.52, G.10
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