IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v10y2007i01ns0219024907004081.html
   My bibliography  Save this article

Pricing Path-Dependent Options On State Dependent Volatility Models With A Bessel Bridge

Author

Listed:
  • GIUSEPPE CAMPOLIETI

    (Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario N2L 3C5, Canada)

  • ROMAN MAKAROV

    (Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario N2L 3C5, Canada)

Abstract

This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, arising as a particular case of these models. The transition p.d.f.s or pricing kernels are mapped onto an underlying simpler squared Bessel process and are expressed analytically in terms of modified Bessel functions. We establish precise links between pricing kernels of such models and the randomized gamma distributions, and thereby demonstrate how a squared Bessel bridge process can be used for exact sampling of the Bessel family of paths. A Bessel bridge algorithm is presented which is based on explicit conditional distributions for the Bessel family of volatility models and is similar in spirit to the Brownian bridge algorithm. A special rearrangement and splitting of the path integral variables allows us to combine the Bessel bridge sampling algorithm with either adaptive Monte Carlo algorithms, or quasi-Monte Carlo techniques for significant numerical efficiency improvement. The algorithms are illustrated by pricing Asian-style and lookback options under the Bessel family of volatility models as well as the CEV diffusion model.

Suggested Citation

  • Giuseppe Campolieti & Roman Makarov, 2007. "Pricing Path-Dependent Options On State Dependent Volatility Models With A Bessel Bridge," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 51-88.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:01:n:s0219024907004081
    DOI: 10.1142/S0219024907004081
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024907004081
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024907004081?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. Albanese, Claudio & Campolieti, Giuseppe, 2005. "Advanced Derivatives Pricing and Risk Management," Elsevier Monographs, Elsevier, edition 1, number 9780120476824.
    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. Makarov Roman N. & Glew Devin, 2010. "Exact simulation of Bessel diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 283-306, January.
    2. Giuseppe Campolieti & Roman N. Makarov & Andrey Vasiliev, 2011. "Bridge Copula Model for Option Pricing," Papers 1110.4669, arXiv.org.
    3. Ian Iscoe & Asif Lakhany, 2011. "Adaptive Simulation of the Heston Model," Papers 1111.6067, arXiv.org.

    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. Giuseppe Campolieti & Roman N. Makarov & Andrey Vasiliev, 2011. "Bridge Copula Model for Option Pricing," Papers 1110.4669, arXiv.org.
    2. Giuseppe Campolieti & Roman Makarov, 2008. "Path integral pricing of Asian options on state-dependent volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 147-161.
    3. Lee, Dongyeol & Kim, Woo Chang, 2021. "Cost of shareholder engagement by institutional investors under short-swing profit rule," Finance Research Letters, Elsevier, vol. 40(C).
    4. Chung-Han Hsieh, 2020. "Generalization of Affine Feedback Stock Trading Results to Include Stop-Loss Orders," Papers 2004.12848, arXiv.org.

    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:10:y:2007:i:01:n:s0219024907004081. 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.