Financial market is a typical complex system because it is an open trading system and behaved by a variety of interacting agents. The consequence of the interaction appears quite complex and nonlinear. Therefore, how to observe this system and find a simplified methodology to describe it is, probably, a key to understand and solve the problem. In this paper, the author observes a stationary transaction volume distribution over a trading price range, studied the relationship between the volume and price of transaction through the amount of it in stock market. The probability of accumulated trading volume (i.e. actual supply/demand quantity or transaction volume) that distributes over a trading price range gradually emerges kurtosis near a transaction price mean value in a transaction body system when it takes a longer trading time, regardless of actual trading price fluctuation path, time series, or total transaction volume in the time interval. The volume and price behaves a probability wave toward an equilibrium price, driven by an actual supply/demand quantity restoring or regressive force that can be represented by a linear potential (an autoregressive item in mathematics). In terms of physics, the author derives a time-independent security transaction probability wave differential equation and obtains an explicit transaction volume distribution function over the price, the distribution of absolute zero-order Bessel eigenfunctions, in a stable transaction body system when its supply and demand quantity is dynamic. By fitting and testing the function with intraday real transaction volume distributions over the price on a considerable number of individual stocks in Shanghai 180 Index, the author demonstrates its validation at this early stage, and attempts to offer a micro and dynamic transaction volume/price (actual supply/demand quantity and price) probability wave theory.

In this paper, the author observes a stationary volume/price pattern, while studying the relationship between volume and price through the amount of transaction in stock market. The probability of accumulated trading volume (actual supply/demand volume) that distributes over its price range gradually emerges the maximum around the price mean value in a transaction body system when it takes a longer trading time regardless of its price fluctuation path or time series in the time interval. The volume/price behaves a probability wave toward an actual supply/demand equilibrium price, forced by a linear central actual supply/demand potential. In terms of physics, the author establishes a transaction (actual supply/demand) energy hypothesis, defines a measurable actual supply/demand restoring force, derives a time-independent security transaction (actual supply/demand) probability wave differential equation, and obtains an explicit volume/price distribution function, the distribution of absolute zero-order Bessel eigenfunctions, in a stable transaction body system when its supply/demand is in a dynamic state. By fitting and testing the function with intraday real transaction volume/price distributions on a considerable number of individual stocks in Shanghai 180 Index, the author demonstrates its validation at this early stage, and attempts to offer a micro and dynamic actual supply/demand volume/price wave theory. JEL classification: G12; D50; C51; C52

In this paper, the author observes a stationary volume/price pattern, while studying the relationship between volume and price through the amount of transaction in stock market. The probability of accumulated trading volume (actual supply/demand volume) that distributes over its price range gradually emerges the maximum around the price mean value in a transaction body system when it takes a longer trading time regardless of its price fluctuation path or time series in the time interval. The volume/price behaves a probability wave toward an actual supply/demand equilibrium price, forced by a linear central actual supply/demand potential. In terms of physics, the author establishes a transaction (actual supply/demand) energy hypothesis, defines a measurable actual supply/demand restoring force, derives a time-independent security transaction (actual supply/demand) probability wave differential equation, and obtains an explicit volume/price distribution function, the distribution of absolute zero-order Bessel eigenfunctions, in a stable transaction body system when its supply/demand is in a dynamic state. By fitting and testing the function with intraday real transaction volume/price distributions on a considerable number of individual stocks in Shanghai 180 Index, the author demonstrates its validation at this early stage, and attempts to offer a micro and dynamic actual supply/demand volume/price wave theory.