In this paper, we study market crowd psychological behaviors in learning by correlation analysis, using every trading high frequency data in China stock market. We introduce a notion of trading conditioning in terms of operant conditioning in psychology and measure its intensity by accumulative trading volume probability in a time interval in the transaction price-volume probability wave equation that can describe market crowd coherence in their interacted trading behavior. We find that there is, in general, significant positive correlation between the rate of price volatility mean return and the change in the intensity of market crowd trading conditioning. They behave significantly disposition effect in stock selling and herd behavior in stock buying with expectation on return simultaneously. Specifically, “the herd” have significant stronger expectation on price momentum than its reversal. Second, there is also a significant negative correlation between them in a subdivided term; market crowd show buy-and-hold behavior when price rises steadily, and panic selling when it drops abruptly in depth. We explain both the puzzle of more peaked, heavily tailed, and clustered characteristics in return distribution by coherence and that of market crowd behavioral “anomalies” by trading conditioning in a unified transaction price-volume probability wave framework.

To brief a transaction volume-price probability wave equation, a new advance in econophysics; To introduce a notion of trading conditioning for the first time in terms of operant conditioning in psychology; To measure the intensity of market crowd’s trading conditioning by transaction volume probability; To test correlation between the rate of mean return and the change in the intensity of trading conditioning subject to the return, using high frequency data in China stock market; To study market crowd’s learning and psychological behavior by correlation analysis, and explain their behavioral“anomalies”by trading conditioning.

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.

We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use transaction volume probability to describe price volatility uncertainty and intensity. Applying the model to high frequent data test in China stock market, we have main findings as follows: 1) there is, in general, significant positive correlation between the rate of mean return and that of change in trading conditioning intensity; 2) it lacks significance in spite of positive correlation in two time intervals right before and just after bubble crashes; and 3) it shows, particularly, significant negative correlation in a time interval when SSE Composite Index is rising during bull market. Our model and findings can test both disposition effect and herd behavior simultaneously, and explain excessive trading (volume) and other anomalies in stock market.

In this paper, the author observes a stationary transaction volume distribution over a trading price range in intraday transactions on individual stocks by studying relationship between the volume and price of transaction through amount of transaction in stock market. The transaction or accumulated trading volume gradually emerges kurtosis near the price mean value over a 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. The volume/price behaves a probability wave toward an equilibrium price, driven by a restoring force that can be represented by a linear potential. In terms of physics, the author derives a time-independent transaction volume/price probability wave equation and gets two sets of analytical transaction volume distribution eigenfunctions over a price range when supply or demand quantity varies. By fitting and testing the functions with intraday real transaction volume distribution over a price range on a considerable number of individual stocks in Shanghai 180 Index, the author shows the existence of relative equilibrium in stock market and demonstrates the model validation at this early stage. It concludes that either General Equilibrium Theory or Price Random Walk Hypothesis is an extreme conditional case in the probability wave model. Thus, the author attempts to offer a unified micro and dynamic probability wave theory on transaction volume/price in financial market. 本文作者通过成交金额研究股票市场中的成交量与价格之间关系时，观察到每只股票全天的成交量（即累计交易量）在交易价格区间有一种平稳的分布关系。随着交易时间的延长，累计交易量在交易价格区间逐渐显现出在成交价格均值附近峰化的分布特征。这一特征与体系在此间交易价格涨落的路径、时间序列或总成交量的大小无关。成交量价的运动表现为能够用线性势表示的中心力的作用下，围绕体系某一均衡价格运动的几率波。由此，作者用物理的方法推导出不显含时间变量的证券成交量价的波动方程并且得到当供求关系变化时，两组解析的成交量随价格变化的分布函数。用该函数与上证180指数中一些股票在全天真实的成交量随价格的分布进行拟合和检验，作者初步证明了在股票市场中存在相对均衡并且验证了该模型的有效性。其结论是：无论一般均衡理论还是价格波动的随机游走假说都是几率波模型在极端条件下的一个特例。这样，作者试图提出一个适用于描述金融市场中统一、微观和动态的成交量价几率波理论。

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.