GARCH Options via Local Risk Minimization

Quantitative Finance, 12(7), 1095-110, 2012

25 Pages Posted: 13 May 2014  

Juan-Pablo Ortega

Universität Sankt Gallen; Centre National de la Recherche Scientifique (CNRS)

Date Written: May 12, 2014


We apply a quadratic hedging scheme developed by Föllmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations. More importantly, since those local risk-minimizing strategies are in general convoluted and difficult to evaluate, we introduce Girsanov-like risk-neutral measures for the log-prices that yield more tractable and useful results. Regarding this subject, we focus on GARCH time series models with Gaussian innovations and we provide specific sufficient conditions that have to do with the finiteness of the kurtosis, under which those martingale measures are appropriate in the context of quadratic hedging. When this equivalent martingale measure is adapted to the price representation we are able to recover out of it the classical pricing formulas of Duan and Heston-Nandi, as well as hedging schemes that improve the performance of those proposed in the literature.

Keywords: GARCH models, option pricing, option hedging, local risk minimization

JEL Classification: C22, C32, C5

Suggested Citation

Ortega, Juan-Pablo, GARCH Options via Local Risk Minimization (May 12, 2014). Quantitative Finance, 12(7), 1095-110, 2012. Available at SSRN:

Juan-Pablo Ortega (Contact Author)

Universität Sankt Gallen ( email )

Bodanstrasse 6
St. Gallen, St. Gallen CH-9000


Centre National de la Recherche Scientifique (CNRS) ( email )

16 route de Gray
Besançon, 25030


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