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.

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.

The trade size Omega has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size Omega for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impact. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r-omega^alpha with alpha=2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation alpha=alpha_omega/alpha_r is verified, where alpha_omega and alpha_r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and Omega for small-size trades. We anticipate that these regularities may hold in other order-driven markets.

随着全球经济一体化进程的加快，和信息技术的广泛使用，全球金融市场的相关性和波动性也日益增强，因此，愈来愈多的学者进入金融市场的研究领域，这其中就有许多的物理学者。他们的加盟，为金融市场的研究带来了新的研究视角、新的研究方法和新的认识，逐渐形成了一门新兴的交叉学科------经济物理学（Econophysics）。