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An option pricing formula for the GARCH diffusion model


Barone-Adesi, Giovanni; Rasmussen, Henrik; Ravanelli, Claudia (2005). An option pricing formula for the GARCH diffusion model. Computational Statistics & Data Analysis, 49(2):287-310.

Abstract

The first four conditional moments of the integrated variance implied by the GARCH diffusionprocess are derived analytically. Based on these moments and on a power series method an analytical approximation formula to price European options under the GARCH diffusion model is obtained. Monte Carlo simulations show that this approximation formula up to order three is accurate for a large set of reasonable parameters and highlight potential instabilities of the fourth term. Finally, the closed-form approximation formula is used to shed light on the qualitative properties of implied volatility surfaces induced by GARCH diffusion models.

Abstract

The first four conditional moments of the integrated variance implied by the GARCH diffusionprocess are derived analytically. Based on these moments and on a power series method an analytical approximation formula to price European options under the GARCH diffusion model is obtained. Monte Carlo simulations show that this approximation formula up to order three is accurate for a large set of reasonable parameters and highlight potential instabilities of the fourth term. Finally, the closed-form approximation formula is used to shed light on the qualitative properties of implied volatility surfaces induced by GARCH diffusion models.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Computational Mathematics
Physical Sciences > Computational Theory and Mathematics
Physical Sciences > Applied Mathematics
Scope:Discipline-based scholarship (basic research)
Language:English
Date:30 April 2005
Deposited On:21 Mar 2023 13:05
Last Modified:28 Jun 2024 01:44
Publisher:Elsevier
ISSN:0167-9473
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.csda.2004.05.014
Official URL:https://www.sciencedirect.com/science/article/pii/S0167947304001483
Other Identification Number:merlin-id:9909
  • Content: Accepted Version
  • Language: English