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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," Papers 1603.05513, arXiv.org.
    • Handle: RePEc:arx:papers:1603.05513
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    File URL: http://arxiv.org/pdf/1603.05513
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