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

Posted: 16 Oct 2008

See all articles by Lars Stentoft

Lars Stentoft

Department of Economics, University of Western Ontario; Center for Interuniversity Research and Analysis on Organization (CIRANO); Aarhus University - CREATES

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Date Written: Fall 2008

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: C22, C53, G13, American options, GARCH models, least squares Monte Carlo method, normal inverse Gaussian distribution

Suggested Citation

Stentoft, Lars, American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution (Fall 2008). Journal of Financial Econometrics, Vol. 6, Issue 4, pp. 540-582, 2008. Available at SSRN: https://ssrn.com/abstract=1281996 or http://dx.doi.org/nbn013

Lars Stentoft (Contact Author)

Department of Economics, University of Western Ontario ( email )

London, Ontario N6A 5B8
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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