IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1635.html
   My bibliography  Save this paper

The Jacobi Stochastic Volatility Model

Author

Listed:
  • Damien Ackerer

    (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute)

  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute)

  • Sergio Pulido

    (Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, UMR CNRS 8071)

Abstract

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form. We use this to derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and forward start options on the underlying return. We derive sharp analytical and numerical bounds on the series truncation errors. We illustrate the performance by numerical examples, which show that our approach offers a viable alternative to Fourier transform techniques.

Suggested Citation

  • Damien Ackerer & Damir Filipović & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Swiss Finance Institute Research Paper Series 16-35, Swiss Finance Institute, revised Jun 2016.
  • Handle: RePEc:chf:rpseri:rp1635
    as

    Download full text from publisher

    File URL: http://ssrn.com/abstract=2782486
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    2. Christa Cuchiero, 2017. "Polynomial processes in stochastic portfolio theory," Papers 1705.03647, arXiv.org.
    3. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    4. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    5. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    6. Cuchiero, Christa, 2019. "Polynomial processes in stochastic portfolio theory," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1829-1872.

    More about this item

    Keywords

    Jacobi process; option pricing; polynomial model; stochastic volatility;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:chf:rpseri:rp1635. 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.

    We have no bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    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.