IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2502.00938.html
   My bibliography  Save this paper

On Noncommutative Quantum Mechanics and the Black-Scholes Model

Author

Listed:
  • Abraham Espinoza-Garc'ia
  • Pablo Vega-Lara
  • Luis Rey D'iaz-Barr'on
  • F. Teodoro Hern'andez Grovas

Abstract

Two novel and direct quantum mechanical representations of the Black-Scholes model are constructed based on the (Wick-rotated) quantization of two specific mechanical systems. The quantum setup is achieved by means of the associated Laplace-Beltrami operator (one for each model), and not by merely applying the usual naive rule. Additionally, the clear identification of the geometric content of the underlying classical framework is exploited in order to arrive at a noncommutative quantum mechanics generalization of the Black-Scholes model. We also consider a system consisting of two degrees of freedom whose (Wick-rotated) quantization leads to a model which can be seen as related to the Merton-Garman family. This model is also generalized via noncommutative quantum mechanics.

Suggested Citation

  • Abraham Espinoza-Garc'ia & Pablo Vega-Lara & Luis Rey D'iaz-Barr'on & F. Teodoro Hern'andez Grovas, 2025. "On Noncommutative Quantum Mechanics and the Black-Scholes Model," Papers 2502.00938, arXiv.org.
    • Handle: RePEc:arx:papers:2502.00938
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2502.00938
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Belal Ehsan Baaquie, 2020. "Mathematical Methods and Quantum Mathematics for Economics and Finance," Springer Books, Springer, number 978-981-15-6611-0, March.
    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. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2024. "Corporate bonds: fixed versus stochastic coupons—an empirical study," Journal of Asset Management, Palgrave Macmillan, vol. 25(1), pages 113-128, February.

    More about this item

    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:arx:papers:2502.00938. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.