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- Title
Efficient Implementation of Tree-Based Option Pricing and Hedging Algorithms under GARCH Models.
- Authors
Guo, Zhiyu; Augustyniak, Maciej; Badescu, Alexandru
- 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, the authors 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. The authors assess the efficiency and accuracy of their approach by computing European style option prices and optimal quadratic hedges derived based on the local-risk minimization criteria under the physical measure. The authors test the effectiveness of their approach relative to the standard mean-tracking tree benchmark using different sets of GARCH parameters. Overall, the authors find that their 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.
- Publication
Journal of Derivatives, 2024, Vol 31, Issue 3, p141
- ISSN
1074-1240
- Publication type
Academic Journal
- DOI
10.3905/jod.2023.1.192