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Modelling Illiquid Stocks Using Quantum Stochastic Calculus

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  • 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.

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

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    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.
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    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.
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