Option Pricing for GARCH-Type Models with Generalized Hyperbolic Innovations

Centre d’Economie de la Sorbonne Working Paper No. 2010.23

31 Pages Posted: 18 Jul 2010

See all articles by Dominique Guegan

Dominique Guegan

Université Paris I Panthéon-Sorbonne

Christophe Chorro

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES)

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES)

Multiple version iconThere are 2 versions of this paper

Date Written: July, 17 2010

Abstract

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets are modeled by GARCH-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk neutral distribution is unique and implies again a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of speci fic parametric innovations to reproduce market prices in the context of an exponential affine speci fication of the stochastic discount factor.

Keywords: Generalized Hyperbolic Distribution, Option Pricing, Incomplete Markets, CAC 40, SP 500, GARCH-Type Models

JEL Classification: G13, C22.

Suggested Citation

Guegan, Dominique and Chorro, Christophe and Ielpo, Florian, Option Pricing for GARCH-Type Models with Generalized Hyperbolic Innovations (July, 17 2010). Centre d’Economie de la Sorbonne Working Paper No. 2010.23, Available at SSRN: https://ssrn.com/abstract=1642098 or http://dx.doi.org/10.2139/ssrn.1642098

Dominique Guegan (Contact Author)

Université Paris I Panthéon-Sorbonne ( email )

106 avenue de lhopital
75634 Paris Cedex 13
Paris, IL
France

Christophe Chorro

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

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