Option pricing for GARCH-type models with generalized hyperbolic innovations
AbstractIn 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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 10023.
Length: 31 pages
Date of creation: Mar 2010
Date of revision:
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Generalized hyperbolic distribution; option pricing; incomplete markets; CAC 40; SP 500; GARCH-type models.;
Other versions of this item:
- Christophe Chorro & Dominique Guégan & Florian Ielpo, 2012. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1079-1094, April.
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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- Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
- Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2011.
"Option pricing with discrete time jump processes,"
Documents de travail du Centre d'Economie de la Sorbonne
11037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2011. "Option pricing with discrete time jump processes," Documents de travail du Centre d'Economie de la Sorbonne 11037r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
- Zhu, Ke & Ling, Shiqing, 2014. "Model-based pricing for financial derivatives," MPRA Paper 56623, University Library of Munich, Germany.
- Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
- Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2012. "Option pricing with discrete time jump processes," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00611706, HAL.
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