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Option pricing under GARCH models with generalized hyperbolic innovations (II) : data and results

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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. The data set is the daily log returns of the French CAC 40 index, on the period January 2, October 26, 2007. Under the historical measure, we estimate an EGARCH model with Generalized Hyperbolic innovations, using this dataset. We showed in Chorro, Guégan and Ielpo (2008) that when the pricing kernel is an exponential affine function of the state variables, the risk neutral distribution is unique and implies again a Generalized Hyperbolic dynamic, with changed parameters. Thus, using this theoretical result associated to Monte Carlo simulations, we compare our 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 the exponential affine specification of the stochastic discount factor.

Suggested Citation

  • Christophe Chorro & Dominique Guegan & Florian Ielpo, 2008. "Option pricing under GARCH models with generalized hyperbolic innovations (II) : data and results," Documents de travail du Centre d'Economie de la Sorbonne b08047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:b08047
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    Cited by:

    1. Chorro, C. & Guégan, D. & Ielpo, F., 2010. "Martingalized historical approach for option pricing," Finance Research Letters, Elsevier, vol. 7(1), pages 24-28, March.
    2. Dominique Guegan & Jing Zang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 777-795.
    3. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2008. "Option pricing under GARCH models with generalized hyperbolic innovations (I) : methodology," Documents de travail du Centre d'Economie de la Sorbonne b08037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    5. Petr Gapko & Martin Šmíd, 2010. "Modeling a Distribution of Mortgage Credit Losses," Working Papers IES 2010/23, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Sep 2010.

    More about this item

    Keywords

    Generalized Hyperbolic Distribution; option pricing; incomplete market; CAC 40; GARCH models.;

    JEL classification:

    • 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; Diffusion Processes
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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