IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00469529.html
   My bibliography  Save this paper

Option pricing for GARCH-type models with generalized hyperbolic innovations

Author

Listed:
  • Christophe Chorro

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Florian Ielpo

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00469529, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00469529
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00469529
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00469529/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    2. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    3. S. Reimann, 2007. "Price dynamics from a simple multiplicative random process model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(4), pages 381-394, April.
    4. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    5. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    6. V. Alfi & L. Pietronero & A. Zaccaria, 2008. "Minimal Agent Based Model For The Origin And Self-Organization Of Stylized Facts In Financial Markets," Papers 0807.1888, arXiv.org.
    7. Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    8. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.
    9. F. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2007. "Statistical regularities in the return intervals of volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 123-133, January.
    10. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    11. Pištěk, Miroslav & Slanina, František, 2011. "Diversity of scales makes an advantage: The case of the Minority Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2549-2561.
    12. Muhammad Zeeshan Younas, 2020. "How Did Risk Management Methods Change After The 2007 Sub-Prime Mortgage Crisis In The United Kingdom?," Bulletin of Business and Economics (BBE), Research Foundation for Humanity (RFH), vol. 9(1), pages 22-31, March.
    13. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    14. G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
    15. Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
    16. Conlon, T. & Ruskin, H.J. & Crane, M., 2007. "Random matrix theory and fund of funds portfolio optimisation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 565-576.
    17. Denis S. Grebenkov & Jeremy Serror, 2014. "Optimal Allocation of Trend Following Strategies," Papers 1410.8409, arXiv.org.
    18. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    19. Ouyang, F.Y. & Zheng, B. & Jiang, X.F., 2014. "Spatial and temporal structures of four financial markets in Greater China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 236-244.
    20. Danilo Delpini & Giacomo Bormetti, 2012. "Stochastic Volatility with Heterogeneous Time Scales," Papers 1206.0026, arXiv.org, revised Apr 2013.

    More about this item

    Keywords

    Generalized hyperbolic distribution; option pricing; incomplete markets; CAC 40; SP 500; GARCH-type models.; Distribution hyperbolique généralisée; prix d'option; marché incomplet; modèle GARCH.;
    All these keywords.

    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:hal:cesptp:halshs-00469529. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.