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Coupled mode theory of stock price formation

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  • Jack Sarkissian

Abstract

We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in phase jitter for eigenstates. We show that the theory reflects very important characteristics of bid and ask dynamics and order density in the order book. Calibration examples are provided for stocks at various time scales. Lastly, this model allows to quantify and measure risk associated with spread and its fluctuations.

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  • Jack Sarkissian, 2013. "Coupled mode theory of stock price formation," Papers 1312.4622, arXiv.org.
    • Handle: RePEc:arx:papers:1312.4622
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    References listed on IDEAS

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    1. Fabien Guilbaud & Huyên Pham, 2012. "Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information," Working Papers hal-00697125, HAL.
    2. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    4. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    5. Fabien Guilbaud & Huy^en Pham, 2012. "Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information," Papers 1205.3051, arXiv.org.
    6. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
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    Cited by:

    1. 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).
    2. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    3. Jack Sarkissian, 2020. "Quantum coupled-wave theory of price formation in financial markets: price measurement, dynamics and ergodicity," Papers 2002.04212, arXiv.org.
    4. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.

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