A Probability-Wave Model of Stock Trading Volume Across Prices

Summary

This paper studies how trading volume is distributed across prices when the total transaction amount is fixed. It reports that, as trading time increases, cumulative volume forms a distribution with a peak in kurtosis near the mean price over the observed price range. The reported pattern is said to be insensitive to the path of price fluctuations, the time series, and total volume within the interval.

To explain this behavior, the authors propose a transaction-energy hypothesis and derive a time-independent equation for a volume-price probability wave, along with two sets of analytical distribution eigenfunctions. An empirical test is said to show market coherence and provide early validation of the model. The account characterizes the work as an early-stage result but supplies no sample description, test design, or quantitative fit statistics. The probability-wave framing is a proposed explanation, and the summary does not establish practical forecasting value or trading applications.

Key ideas

• The paper examines how trading volume is distributed over a price range when transaction amount is fixed.
• It reports a cumulative volume concentration near the mean price that emerges over longer trading time.
• The reported pattern is described as insensitive to price path, time series, and total volume.
• A transaction-energy hypothesis motivates a time-independent probability-wave equation and analytical distribution functions.
• The empirical evidence is presented as early validation, with limited methodological detail in the document.

Tags

# Does Security Transaction Volume-Price Behavior Resemble a Probability Wave?


# Does Security Transaction Volume-Price Behavior Resemble a Probability Wave?









Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We find that accumulative trading volume gradually emerges a kurtosis near the price mean value over a trading price range when it takes a longer trading time, regardless of actual price fluctuation path, time series, or total transaction volume in the time interval. To explain the volume-price behavior, we, in terms of physics, propose a transaction energy hypothesis, derive a time-independent transaction volume-price probability wave equation, and get two sets of analytical volume distribution eigenfunctions over a trading price range. By empiric test, we show the existence of coherence in stock market and demonstrate the model validation at this early stage. The volume-price behaves like a probability wave.

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