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Quantum coupled-wave theory of price formation in financial markets: Price measurement, dynamics and ergodicity

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  • Sarkissian, Jack

Abstract

We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are represented by eigenvalues of a 2x2 price operator corresponding to “bid” and “ask” eigenstates, while randomness of price operator results in price fluctuations that destroy oscillatory effects. We show that this theory adequately captures behavior of bid–ask spread and allows to model bid and ask price dynamics in a coordinated way. We also discuss ergodicity properties of price formation and show how directional price movement occurs due to ergodicity violation in a quantum process instead of the commonly believed forces acting on price. This theory has wide range of applications such as trade execution modeling, large order pricing and risk valuation for illiquid securities.

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  • Sarkissian, Jack, 2020. "Quantum coupled-wave theory of price formation in financial markets: Price measurement, dynamics and ergodicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120300911
    DOI: 10.1016/j.physa.2020.124300
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    References listed on IDEAS

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    1. Hirshleifer,Jack & Glazer,Amihai & Hirshleifer,David, 2005. "Price Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521523424.
    2. Charles R. Plott & Kirill Pogorelskiy, 2017. "Call Market Experiments: Efficiency and Price Discovery through Multiple Calls and Emergent Newton Adjustments," American Economic Journal: Microeconomics, American Economic Association, vol. 9(4), pages 1-41, November.
    3. Halperin, Igor & Dixon, Matthew, 2020. "“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    5. Caginalp, Carey & Caginalp, Gunduz, 2019. "Price equations with symmetric supply/demand; implications for fat tails," Economics Letters, Elsevier, vol. 176(C), pages 79-82.
    6. Jack Sarkissian, 2013. "Coupled mode theory of stock price formation," Papers 1312.4622, arXiv.org.
    7. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.
    8. Orrell, David, 2020. "A quantum model of supply and demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
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    Cited by:

    1. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.

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