IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.05243.html
   My bibliography  Save this paper

Modelling Illiquid Stocks Using Quantum Stochastic Calculus

Author

Listed:
  • Will Hicks

Abstract

Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical Black-Scholes framework by incorporating a breakdown in the liquidity of a traded asset. This is captured via the widening of the bid offer spread, and the impact on the nature of the resulting probability distribution is modelled in this work.

Suggested Citation

  • Will Hicks, 2023. "Modelling Illiquid Stocks Using Quantum Stochastic Calculus," Papers 2302.05243, arXiv.org.
    • Handle: RePEc:arx:papers:2302.05243
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.05243
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Will Hicks, 2018. "PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation," Papers 1812.00839, arXiv.org, revised Jan 2019.
    2. Will Hicks, 2019. "Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion," Papers 1911.11475, arXiv.org, revised Jan 2020.
    3. Will Hicks, 2018. "Nonlocal Diffusions and The Quantum Black-Scholes Equation: Modelling the Market Fear Factor," Papers 1806.07983, arXiv.org, revised Jun 2018.
    4. Will Hicks, 2019. "A Nonlocal Approach to The Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometry," Papers 1905.07257, arXiv.org.
    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. Will Hicks, 2024. "Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution," Papers 2407.04520, 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. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    2. Will Hicks, 2019. "Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion," Papers 1911.11475, arXiv.org, revised Jan 2020.
    3. Anantya Bhatnagar & Dimitri D. Vvedensky, 2022. "Quantum effects in an expanded Black–Scholes model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-12, August.
    4. Will Hicks, 2024. "Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems," Papers 2406.20027, arXiv.org.
    5. Will Hicks, 2023. "Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods," Papers 2302.05256, arXiv.org.
    6. Yeşiltaş, Özlem, 2023. "The Black–Scholes equation in finance: Quantum mechanical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    7. Din Prathumwan & Kamonchat Trachoo, 2019. "Application of the Laplace Homotopy Perturbation Method to the Black–Scholes Model Based on a European Put Option with Two Assets," Mathematics, MDPI, vol. 7(4), pages 1-11, March.
    8. Will Hicks, 2021. "Wild Randomness, and the application of Hyperbolic Diffusion in Financial Modelling," Papers 2101.04604, arXiv.org, revised Apr 2021.

    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:2302.05243. 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.