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Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations

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Author Info

  • Christophe Chorro

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Dominique Guegan

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Florian Ielpo

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00511965.

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Date of creation: 2012
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Publication status: Published, Quantitative Finance, 2012, 12, 7, 1079-1094
Handle: RePEc:hal:cesptp:hal-00511965

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Related research

Keywords: Generalized hyperbolic distribution; Option pricing; Incomplete markets; CAC 40; SP 500; GARCH-type models;

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Cited by:
  1. Zhu, Ke & Ling, Shiqing, 2014. "Model-based pricing for financial derivatives," MPRA Paper 56623, University Library of Munich, Germany.
  2. 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.
  3. 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.
  4. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.

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