Efficient Implementation of Tree-Based Option Pricing and Hedging Algorithms under GARCH Models

Abstract

This article explores the use of lattice-based approximation schemes for pricing and hedging financial derivatives under GARCH models. The explosion problem and the computational cost associated with the implementation of GARCH-based trees have been well documented in the literature. To address these shortcomings, we propose a truncated mean-tracking tree that limits the number of nodes generated within the tree, focusing only on the relevant state space of the GARCH model. We assess the efficiency and accuracy of our approach by computing European style option prices and optimal quadratic hedges derived based on the local-risk minimization criteria under the physical measure. We test the effectiveness of our approach relative to the standard mean-tracking tree benchmark using different sets of GARCH parameters. Overall, we find that our truncation strategy significantly reduces the computational cost of implementing the tree, without sacrificing its accuracy, the largest gains being noticed for longer-term maturity contracts.