Abstract

Manipulation is an important issue for both developed and emerging stock markets. Many efforts have been made to detect manipulation in stock markets. However, it is still an open problem to identify the fraudulent traders, especially when they collude with each other. In this paper, we focus on the problem of identifying the anomalous traders using the transaction data of eight manipulated stocks and forty-four non-manipulated stocks during a one-year period. By analyzing the trading networks of stocks, we find that the trading networks of manipulated stocks exhibit significantly higher degree-strength correlation than the trading networks of non-manipulated stocks and the randomized trading networks. We further propose a method to detect anomalous traders of manipulated stocks based on statistical significance analysis of degree-strength correlation. Experimental results demonstrate that our method is effective at distinguishing the manipulated stocks from non-manipulated ones. Our method outperforms the traditional weight-threshold method at identifying the anomalous traders in manipulated stocks. More importantly, our method is difficult to be fooled by colluded traders.

Introduction

Stock market provides companies with a place to raise money and allows the investors to trade their shares conveniently. Generally speaking, the price of a stock reflects the common judgment to the value of the stock and it is determined by the supply and demand of the stock if without any interference. However, stock prices could be manipulated by spurious information and fraudulent trades. Manipulation of stock prices affects investors’ confidence, disturbs the market order and is harmful to the development of stock markets. Therefore, manipulation is an important issue for both developed and emerging stock markets.

The pioneering work of stock price manipulation classified the manipulations into three types: action-based manipulation, information-based manipulation and trade-based manipulation [1]. [2]. Earlier studies mainly investigated the action-based and information-based manipulation, such as insider dealing [3]. [4]. Recent research interests focused on the trade-based manipulation, which is more common in current stock markets. Güray Küçükkocaoğlu examined the closing-price manipulation in the Istanbul Stock Exchange [5]. Aggarwal and Wu developed a model to explain trade-based manipulation and tested the model using data from US stock markets [6]. Sun et al. investigated the statistical properties of trading activity and pointed out the differences between non-manipulated stocks and manipulated stocks [7] .

Recently, the detection of manipulation has attracted much research attention. Most approaches adopted the supervised learning framework in which detection models are trained using the transactions which have been carefully judged as anomalous or normal ones a priori. Palshikar and Bahulkar attempted to identify the pattern of manipulation using fuzzy temporal logic [8]. Öğüt et al. detected stock price manipulation using artificial neural networks and support vector machine [9]. However, the supervised learning framework depends heavily on the quality and size of training data, which is very difficult to obtain in practice. Alternatively, several other methods, such as clustering technique and statistical method, were employed to detect manipulation. Palshikar and Apte applied graph clustering techniques to detect the candidate collusion sets [10]. Sun et al. investigated the detection of trade-based manipulation in Chinese stock markets by analyzing trading networks [11] .

Although many efforts have been made to detect manipulation, it is still an open problem to identify the fraudulent traders, especially when they collude with each other. In trade-based manipulation, a group of colluded traders acts together to create an artificial demand for the stock and attracts other investors to buy the stock. In this way, the group of traders can make profit by selling their shares when the stock price rises sufficiently. The manipulation from colluded traders appears frequently in emerging stock markets, such as Chinese stock market, where a single trader can control thousands of accounts. In addition, such type of manipulation usually lasts for a long time. This poses a big challenge to the surveillance systems of exchange, which only analyze short-term transaction data in the limited time.

In this paper, we focus on the problem of identifying the anomalous traders using the transaction data. For each stock, we construct a stock trading network which depicts the frequency of transaction among traders. By analyzing the correlation between degree and strength of nodes in the stock trading network, we find that the non-manipulated stocks behave almost identically to their randomized counterparts while the manipulated stocks perform very differently. Motivated by this finding, we take the randomized network as null model and then identify the anomalous traders by checking the statistical significance of the ratio of strength to degree. We test our method on 44 non-manipulated stocks and 8 manipulated stocks from Chinese stock market. Results demonstrate the effectiveness of our method at distinguishing the manipulated stocks from non-manipulated ones. Moreover, our method outperforms the traditional weight-threshold method at identifying the anomalous traders in manipulated stocks.

Results

The stock trading network

Promoted by the success of network theory in many interdisciplinary fields [12] –[16]. network has been increasingly used to investigate the financial systems. For example, much research attention has been paid to investigate stock markets from the perspective of complex networks [17] –[25]. In recent years, with the increasing availability of transaction data to researchers, stock trading network is taken as a convenient tool to characterize the trading relationships among traders in stock markets. Similar to complex networks from other fields, stock trading network also possesses a power-law degree distribution, a power-law strength distribution, and a power-law weight distribution [11]. [26] .

Before proceeding, we first introduce two types of widely-used stock trading networks, namely trading volume network and trading times network. Nodes in the two types of stock trading networks correspond to traders involved in the transactions of stock. An edge connects two traders who appear in a transaction. The weight of edge, however, has different physical meanings for the two types of trading networks. For trading volume networks, the weight of en edge represents the volume of the transactions among traders. For trading times network, the weight of edge describes the number of times two traders appear in the same transaction. In this paper, we focus on the trading times network and hereafter we use trading network to refer to the trading times network for convenience. In addition, we use the daily trading network to refer to the trading network constructed according to the transactions in one transaction day. Accordingly, we use the yearly trading network to refer to the trading network constructed according to the transactions in a whole year.

In general, the properties of trading network depend heavily on the trading rules regulated by the stock exchange. Thus, we also briefly introduce the trading rules in stock market. In stock market, a trader submits bid/ask orders to the electronic trading system when he/she wants to buy/sell shares. In the trading system, the list of bid orders is sorted in descending order of price and the list of ask orders is sorted in ascending order of price. For each of the two lists of orders, two orders with the same price are sorted according to their submission time. The trading system matches a bid order and an ask order from the top of these two lists. Once a bid order is matched by an ask order, a transaction is executed. If the two matched orders do not have the same volume, the unexecuted part of the order with larger volume is taken as a new order added to in the corresponding list. As an example, Figure 1 gives an illustration of the trading rule in stock market.

An example of the order matching process by electronic system in stock exchange.

Correlation between strength and degree in trading network

The degree-strength correlation for eight manipulated stocks.

We have shown that the manipulated stocks exhibit higher exponents of the power-law degree-strength correlation function. This implies that the weight of edges depend on the degree of nodes to some extent. One possible explanation is that anomalous traders trade more often among themselves to influence the volume and the price of the target stock. More importantly, the higher edge weight can be attributed to the colluded traders with low degree. These traders deceive the electronic systems in Stock Exchange and form intentional trades among themselves. Their trading behavior may give rise to nonlinear degree-strength correlation among traders with low degree. In sum, the nonlinear degree-strength correlation in manipulated stock networks provides us important clues to identify the anomalous traders and motivates us to use the ratio of strength to degree to identify these anomalous traders in manipulated stocks.

Identifying anomalous traders by statistical significance

To use the method of statistical significance, we should first choose an appropriate null mode for each trading network. Here, the adopted null model is a randomized network with no correlation between node strength and node degree. The randomized network is obtained by retaining the topology of the original trading network and redistributing the weights of edges randomly. For convenience, for node with degree and strength , we use to denote its ratio of strength to degree. Figure 4 shows the distribution of for two trading networks and their randomized counterparts. One trading network is the network for a non-manipulated stock and the other is for a manipulated stock. From Figure 4. we can see that the ratio of strength to degree roughly follows a normal distribution for the two randomized networks. The average of for the randomized networks is and the standard deviation can be easily obtained. For a node in a trading network, we can compute the z-score as . The node is viewed as candidate anomalous trader if its z-score is larger than 3, which corresponds to the statistical significance level 0.001.