Implied GARCH Volatility Forecasting

25 Pages Posted: 19 Feb 2002

See all articles by Thorsten Lehnert

Thorsten Lehnert

University of Luxembourg

Cyriel de Jong

Erasmus University Rotterdam (EUR) - Department of Financial Management; Erasmus Research Institute of Management (ERIM)

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

Suggested Citation

Lehnert, Thorsten and De Jong, Cyriel, Implied GARCH Volatility Forecasting (December 2001). Available at SSRN: or

Thorsten Lehnert

University of Luxembourg ( email )

6, rue Coudenhove-Kalergi
Luxembourg, L-1359

Cyriel De Jong (Contact Author)

Erasmus University Rotterdam (EUR) - Department of Financial Management ( email )

P.O. Box 1738
Room T09-53
3000 DR Rotterdam
+31 10 408 2300 (Phone)
+31 10 408 9017 (Fax)

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam

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