Option Pricing for Garch-Type Models with Generalized Hyperbolic Innovations

30 Pages Posted: 24 Oct 2010

See all articles by Florian Ielpo

Florian Ielpo

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

Dominique Guegan

Université Paris I Panthéon-Sorbonne

Christophe Chorro

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

Multiple version iconThere are 2 versions of this paper

Date Written: October 22, 2010

Abstract

In this paper, we provide a new dynamic asset pricing model for plain vanilla options on equity option indexes. 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 specific parametric innovations to reproduce market prices in the context of an exponential affine specification 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

Ielpo, Florian and Guegan, Dominique and Chorro, Christophe, Option Pricing for Garch-Type Models with Generalized Hyperbolic Innovations (October 22, 2010). Paris December 2010 Finance Meeting EUROFIDAI - AFFI. Available at SSRN: https://ssrn.com/abstract=1695864 or http://dx.doi.org/10.2139/ssrn.1695864

Florian Ielpo (Contact Author)

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

106-112 Boulevard de l'hopital
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Unigestion ( email )

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Dominique Guegan

Université Paris I Panthéon-Sorbonne ( email )

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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

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