IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v15y2008i2p151-181.html
   My bibliography  Save this article

Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree

Author

Listed:
  • Ionuţ Florescu
  • Frederi Viens

Abstract

The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous-time SV models are provided. Classical arbitrage-free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue-chip stocks. Results obtained here are compared with those from non-random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option.

Suggested Citation

  • Ionuţ Florescu & Frederi Viens, 2008. "Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 151-181.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:151-181
    DOI: 10.1080/13504860701596745
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701596745
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/13504860701596745?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.

    Citations

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


    Cited by:

    1. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    2. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    3. Lorenzo Reus & Guillermo Alexander Sepúlveda-Hurtado, 2023. "Foreign exchange trading and management with the stochastic dual dynamic programming method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.
    4. Bowei Chen & Jun Wang, 2014. "A lattice framework for pricing display advertisement options with the stochastic volatility underlying model," Papers 1409.0697, arXiv.org, revised Dec 2015.
    5. Maya Briani & Lucia Caramellino & Antonino Zanette, 2017. "A hybrid approach for the implementation of the Heston model," Post-Print hal-00916440, HAL.
    6. Ha-Young Kim & Frederi Viens, 2012. "Portfolio optimization in discrete time with proportional transaction costs under stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 405-425, May.
    7. Duy Nguyen, 2018. "A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-30, December.
    8. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2024. "Option Pricing Using a Skew Random Walk Binary Tree," JRFM, MDPI, vol. 17(4), pages 1-29, March.
    9. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.
    10. Xiao, Chang & Florescu, Ionut & Zhou, Jinsheng, 2020. "A comparison of pricing models for mineral rights: Copper mine in China," Resources Policy, Elsevier, vol. 65(C).

    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:apmtfi:v:15:y:2008:i:2:p:151-181. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.