Lattice-Based Hedging Schemes Under GARCH Models

27 Pages Posted: 6 May 2020 Last revised: 10 Feb 2021

See all articles by Maciej Augustyniak

Maciej Augustyniak

University of Montreal - Department of Mathematics and Statistics

Alexandru Badescu

University of Calgary

Zhiyu Guo

Nankai University

Date Written: November 30, 2020

Abstract

This paper proposes an efficient way to implement quadratic hedging schemes for European options when the asset return process follows an asymmetric non-affine GARCH model driven by Gaussian innovations. More specifically, using a lattice approximation for the underlying, we construct locally risk-minimizing (LRM) hedge ratios under both physical and risk-neutral measures, as well as standard delta strategies. We investigate the convergence of option prices and hedges resulting from the LRM strategies relative to the number of intra-daily periods used in the lattice. Several numerical experiments are conducted to assess the sensitivity of the hedge ratios to the equity risk premium and leverage effect parameters, and to compare their performance by computing the corresponding one-period and terminal hedging errors. Our results suggest that the LRM scheme under the physical measure consistently outperforms competing hedging strategies.

Keywords: Option Pricing and Hedging, Local Risk-Minimization, Non-Affine GARCH, Lattice Approximation, Mean-Tracking Tree

JEL Classification: C22, C61, G32

Suggested Citation

Augustyniak, Maciej and Badescu, Alexandru and Guo, Zhiyu, Lattice-Based Hedging Schemes Under GARCH Models (November 30, 2020). Available at SSRN: https://ssrn.com/abstract=3581863 or http://dx.doi.org/10.2139/ssrn.3581863

Maciej Augustyniak (Contact Author)

University of Montreal - Department of Mathematics and Statistics ( email )

C.P. 6128, succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

HOME PAGE: http://dms.umontreal.ca/

Alexandru Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Zhiyu Guo

Nankai University ( email )

94 Weijin Road
Tianjin, 300071
China

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