IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v12y2012i7p1079-1094.html
   My bibliography  Save this article

Option pricing for GARCH-type models with generalized hyperbolic innovations

Author

Listed:
  • Christophe Chorro
  • Dominique Guégan
  • Florian Ielpo

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 being 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 again implies 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 with natural competitors in order to test its efficiency. More generally, our empirical investigations analyse the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1079-1094 DOI: 10.1080/14697688.2010.493180
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2010.493180
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. B. Tóth & F. Lillo & J. D. Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 235-243, November.
    2. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
    3. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, pages 895-953.
    4. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    5. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    6. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    7. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    8. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
    9. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Szabolcs Mike, 2006. "Market efficiency and the long-memory of supply and demand: is price impact variable and permanent or fixed and temporary?," Quantitative Finance, Taylor & Francis Journals, pages 107-112.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, pages 2417-2445.
    2. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Guo, Zi-Yi, 2017. "Empirical Performance of GARCH Models with Heavy-tailed Innovations," EconStor Preprints 167626, ZBW - German National Library of Economics.
    4. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effects in the Returns of US Equities," Documents de travail du Centre d'Economie de la Sorbonne 14022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    5. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
    6. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    7. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01244239, HAL.
    8. repec:hal:journl:halshs-00611706 is not listed on IDEAS
    9. Badescu, Alexandru & Cui, Zhenyu & Ortega, Juan-Pablo, 2016. "A note on the Wang transform for stochastic volatility pricing models," Finance Research Letters, Elsevier, vol. 19(C), pages 189-196.
    10. Fengler, Matthias & Melnikov, Alexander, 2017. "GARCH option pricing models with Meixner innovations," Economics Working Paper Series 1702, University of St. Gallen, School of Economics and Political Science.
    11. 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.
    12. repec:hal:journl:halshs-00973922 is not listed on IDEAS
    13. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Documents de travail du Centre d'Economie de la Sorbonne 14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1079-1094. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.