Quadratic Hedging Schemes for Non-Gaussian GARCH Models

26 Pages Posted: 27 Sep 2012 Last revised: 13 May 2014

Alex Badescu

University of Calgary

Robert J. Elliott

University of Calgary - Haskayne School of Business; University of Alberta - Department of Mathematical and Statistical Sciences

Juan-Pablo Ortega

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

Date Written: September 26, 2012

Abstract

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European Call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.

Keywords: GARCH models, hedging scheme, local risk minimization, conditional Esscher transform, Extended Girsanov Principle, bivariate diffusion limit, minimum variance hedge

JEL Classification: C22, C32, C5

Suggested Citation

Badescu, Alex and Elliott, Robert J. and Ortega, Juan-Pablo, Quadratic Hedging Schemes for Non-Gaussian GARCH Models (September 26, 2012). Journal of Economic Dynamics and Control, Vol. 32, 13-32, 2014. Available at SSRN: https://ssrn.com/abstract=2152462 or http://dx.doi.org/10.2139/ssrn.2152462

Alex Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Robert James Elliott

University of Calgary - Haskayne School of Business ( email )

2500 University Drive, NW
Calgary, Alberta T2N 1N4
Canada

University of Alberta - Department of Mathematical and Statistical Sciences ( email )

Edmonton, Alberta T6G 2G1
Canada
403-492-5811 (Phone)
403-492-6826 (Fax)

Juan-Pablo Ortega (Contact Author)

Universität Sankt Gallen ( email )

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

HOME PAGE: http://juan-pablo-ortega.com

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

16 route de Gray
Besançon, 25030
France

HOME PAGE: http://juan-pablo-ortega.com

Paper statistics

Downloads
77
Rank
259,993
Abstract Views
451