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The Geometric Phase of Stock Trading

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  • Claudio Altafini

Abstract

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

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  • Claudio Altafini, 2016. "The Geometric Phase of Stock Trading," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-13, August.
    • Handle: RePEc:plo:pone00:0161538
    DOI: 10.1371/journal.pone.0161538
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    1. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    2. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    3. Carrion, Allen, 2013. "Very fast money: High-frequency trading on the NASDAQ," Journal of Financial Markets, Elsevier, vol. 16(4), pages 680-711.
    4. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2013. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88, December.
    5. Menkveld, Albert J., 2013. "High frequency trading and the new market makers," Journal of Financial Markets, Elsevier, vol. 16(4), pages 712-740.
    6. Jonathan Brogaard & Terrence Hendershott & Ryan Riordan, 2014. "High-Frequency Trading and Price Discovery," The Review of Financial Studies, Society for Financial Studies, vol. 27(8), pages 2267-2306.
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