IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v06y2003i08ns0219024903002249.html
   My bibliography  Save this article

The Pricing Of Exotic Options By Monte–Carlo Simulations In A Lévy Market With Stochastic Volatility

Author

Listed:
  • WIM SCHOUTENS

    (K. U. Leuven, W. De Croylaan 54, B-3001 Leuven, Belgium)

  • STIJN SYMENS

    (University of Antwerp, Middelheimlaan 1, B-2020 Antwerpen, Belgium)

Abstract

Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of control variates. It turns out that there are significant differences with the classical Black–Scholes prices.

Suggested Citation

  • Wim Schoutens & Stijn Symens, 2003. "The Pricing Of Exotic Options By Monte–Carlo Simulations In A Lévy Market With Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 839-864.
  • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:08:n:s0219024903002249
    DOI: 10.1142/S0219024903002249
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024903002249
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0219024903002249?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Neil Shephard & Ole E. Barndorff-Nielsen, 2001. "Integrated OU Processes and non-Gaussian OU-based stochastic volatility models," Economics Series Working Papers 2001-W01, University of Oxford, Department of Economics.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Integrated OU Processes," Economics Papers 2001-W1, Economics Group, Nuffield College, University of Oxford.
    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. Keegan Mendonca & Vasileios E. Kontosakos & Athanasios A. Pantelous & Konstantin M. Zuev, 2018. "Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation," Papers 1803.03364, arXiv.org, revised Mar 2018.
    2. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    3. Wendong Zheng & Chi Hung Yuen & Yue Kuen Kwok, 2016. "Recursive Algorithms For Pricing Discrete Variance Options And Volatility Swaps Under Time-Changed Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-29, March.
    4. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    5. Gong, Xiaoli & Zhuang, Xintian, 2016. "Option pricing for stochastic volatility model with infinite activity Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 1-10.
    6. Gabriela Pesce & Florencia Verónica Pedroni & Etelvina Chávez & María de la Paz Moral & María Andrea Rivero, 2021. "Exotic options: conceptualization and evolution in the literature from a systematic review," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 95, pages 231-275, July-Dece.
    7. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    8. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.

    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. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
    2. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Higher order variation and stochastic volatility models," Economics Papers 2001-W8, Economics Group, Nuffield College, University of Oxford.
    4. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    5. Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 409-418, February.
    6. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.

    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:wsi:ijtafx:v:06:y:2003:i:08:n:s0219024903002249. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.