Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations

Christophe Chorro (), Dominique Guegan () and Florian Ielpo
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Christophe Chorro: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Dominique Guegan: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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 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 (search for similar items in EconPapers)
Date: 2012
Note: View the original document on HAL open archive server: https://hal.science/hal-00511965v1
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Citations: View citations in EconPapers (27)

Published in Quantitative Finance, 2012, 12 (7), pp.1079-1094. ⟨10.1080/14697688.2010.493180⟩

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Related works:
Working Paper: Option pricing for GARCH-type models with generalized hyperbolic innovations (2010)
Working Paper: Option pricing for GARCH-type models with generalized hyperbolic innovations (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00511965

DOI: 10.1080/14697688.2010.493180

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