Lattice-Based Hedging Schemes Under GARCH Models

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