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Journal of Financial Econometrics Advance Access published online on September 19, 2008
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbn013
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution

Lars Stentoft
     HEC Montréal

Address correspondence to Lars Stentoft, 3000 chemin de la Cote-Sainte Catherine, Montreal (Quebec) Canada H3T 2A7, or e-mail: lars.stentoft{at}hec.ca.

JEL Classification: C22, C53, G13


  Abstract

In this paper we propose a feasible way to price American options in a model with time-varying volatility and conditional skewness and leptokurtosis, using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk-neutral dynamics can be obtained in this model, we interpret the effect of the risk-neutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model out-performs the Gaussian case for pricing options on the three large US stocks as well as a major index. In particular, improvements are found when it comes to explaining the smile in implied standard deviations.

KEYWORDS: American options, GARCH models, least squares Monte Carlo method, normal inverse Gaussian distribution

The author thanks two anonymous referees, an anonymous associate editor, and the co-editor George Tauchen for valuable comments and suggestions. The author also thanks participants at the Third Nordic Econometric Meeting and the Montréal Actuarial and Financial Mathematics Day, participants and discussants at the 2006 SCSE and NFA meetings, as well as seminar participants at HEC Montréal and Brock University. Financial support from the Danish Social Science Research Council (Grant 95015328), the Institut de Finance Mathématique de Montréal (IFM2), and the Center for Econometric Analysis of Time Series (CREATES, funded by the Danish National Research Foundation) is gratefully appreciated.

Received November 12, 2007; revised July 12, 2008; accepted August 4, 2008


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