مدل سازی محاسباتی عامل محور از رابطه قیمت سهام با حجم سهام

From the perspective of the agent-based model of stock markets, this paper examines the possible explanations for the presence of the causal relation between stock returns and trading volume. Using the agent-based approach, we find that the explanation for the presence of the stock price–volume relation may be more fundamental. Conventional devices such as information asymmetry, reaction asymmetry, noise traders or tax motives are not explicitly required. In fact, our simulation results show that the stock price–volume relation may be regarded as a generic property of a financial market, when it is correctly represented as an evolving decentralized system of autonomous interacting agents. One striking feature of agent-based models is the rich profile of agents' behavior. This paper makes use of the advantage and investigates the micro–macro relations within the market. In particular, we trace the evolution of agents' beliefs and examine their consistency with the observed aggregate market behavior. We argue that a full understanding of the price–volume relation cannot be accomplished unless the feedback relation between individual behavior at the bottom and aggregate phenomena at the top is well understood.

The agent-based modeling of stock markets, which originated at the Santa Fe Institute [2] and [47], is a fertile and promising field that can be thought of as a subfield of agent-based computational economics (ACE).1Up to the present, most of the research efforts have been devoted to the analysis of the price dynamics and/or market efficiency of the artificial markets (e.g. [13], [14], [44] and [57]). Some studies have focused on the price deviation or mispricing in the artificial stock markets (e.g. [2], [8], [10], [12], [43], [44], [47] and [56]). Some have gone further to explore the corresponding micro-structure of the markets, such as the aspect of traders' beliefs and behavior (e.g. [11], [13] and [14]). Nevertheless, few have ever visited the univariate dynamics of trading volume series [43] and [56], and, to our best knowledge, none has addressed joint dynamics with prices. 2 As Ying [58] noted almost 40 years ago, stock prices and trading volume are joint products from one single market mechanism. He argued that “any model of the stock market which separates prices from volume or vice versa will inevitably yield incomplete if not erroneous results” [58, p. 676]. In similar vein, Gallant et al. [25] also asserted that researchers can learn more about the very nature of stock markets by studying the joint dynamics of prices in conjunction with volume, instead of focusing on price dynamics alone. As a result, the stock price–volume relation has been an interesting subject in financial economics for many years. 3 While most of the earlier empirical work focused on the contemporaneous relation between trading volume and stock returns, some more recent studies began to address the dynamic relation, i.e. causality, between daily stock returns and trading volume following the notion of Granger causality proposed by Wiener [55] and Granger [27]. In many cases, a bi-directional Granger causality (or a feedback relation) was found to exist in the stock price–volume relation, although some other studies could only find evidence of a uni-directional causality: Either returns would Granger-cause trading volume, or the opposite situation would prevail [1], [37], [48], [49] and [51]. As noted by Granger [28], Hsieh [35], and many others, we live in a world which is “almost certainly nonlinear”. We cannot be satisfied with only exploring the linear causality between stock prices and trading volume. Nonlinear causality would naturally be the next step to pursue. Baek and Brock [3] argued that traditional Granger causality tests based on vector autoregression (VAR) models might overlook significant nonlinear relations. As a result, they proposed a nonlinear Granger causality test by using nonparametric estimators of temporal relations within and across time series. This approach can be applied to any two stationary, mutually independent and individually i.i.d. series. Hiemstra and Jones [32] modified their test slightly to allow the two series under consideration to display “weak (or short-term) temporal dependence”. Several researchers have already adopted this modified Baek and Brock test to uncover price and volume causal relation in real world financial markets [23], [32] and [50]. In most of the cases, they found bi-directional nonlinear Granger causality in the prices and trading volume. In other words, not only did stock returns Granger-cause trading volume, but trading volume also Granger-caused stock returns. The significance of this finding is that trading volume can help predict stock returns, or as an old Wall Street adage goes, “It takes volume to make price move”. There are several possible explanations for the presence of a causal relation between stock returns and trading volume in the literature. First, Epps [20] gave an explanation based on the asymmetric reaction of two groups of investors––“bulls” and “bears”––to the positive information and negative information. The second explanation, which is referred to as the mixture of distributions hypothesis, considers special distributions of speculative prices. For example, Epps and Epps [21] derived a model in which trading volume is used to measure disagreement among traders concerning their beliefs with regard to the variance of the price changes. On the other hand, in Clark's [16] mixture of distributions model, the speed of information flow is a latent common factor which influences stock returns and trading volume simultaneously. A third explanation is the sequential arrival of information models (see, for example, Copeland [17], He and Wang [31], Jennings et al. [38], and Morse [46]). In this asymmetric information world, traders possess differential pieces of new information in the beginning. Before the final complete information equilibrium is achieved, the information is disseminated to different traders only gradually and sequentially. This implies a positive relationship between price changes and trading volume. Lakonishok and Smidt [41] proposed still another model which involves tax- and nontax-related motives for trading. For the sake of window dressing, portfolio rebalancing, or the optimal timing for capital gains, traders may have some special kinds of trading behavior. As a result, Lakonishok and Smidt [41] showed that current trading volume can be related to past price changes because of these motives. In moving away from the traditional representative agent models stated above, recent theoretical works have started to model financial markets with heterogeneous traders. Besides informed traders (insiders), DeLong et al. [18] introduced noise traders with positive-feedback trading strategies into their model. Noise traders do not have any information about the fundamentals and trade solely based on past price movements. As a result, a positive causal relation from stock returns to trading volume appears. In Brock's [5] nonlinear theoretical noise trading model, the estimation errors made by different groups of traders are correlated. Under these settings, he could find that stock price movements and volatilities are related nonlinearly to volume movements. Campbell et al. [6] developed another heterogeneous agent model, in which there are two different types of risk-averse traders. In their frameworks, they are able to explain the autocorrelation properties of stock returns in terms of a nonlinear relation with trading volume. In light of these explanations, this paper attempts to see whether we can replicate the causal relation between stock returns and trading volume via the agent-based stock markets (ABSMs). We consider the agent-based model of stock markets to be highly relevant to this issue. First, the existing explanations mentioned above were based on assumptions either related to the information dissemination schemes or to the traders' reaction styles in regard to information arrival. Since both of these factors are well encapsulated in ABSMs, it is interesting to see whether ABSMs are able to replicate the causal relation. Secondly, information dissemination schemes and traders' behavior are known as emergent phenomena in ABSMs. In other words, these factors are endogenously generated rather than exogenously imposed. This feature can allow us to search for a fundamental explanation for the causal relation. For example, we can ask, “without the assumption of information asymmetry, reaction asymmetry, or noise traders, and so on, can we still have the causal relation?” Briefly, “is the causal relation a generic phenomenon?” Thirdly, we claim that the agent-based models of financial markets are “true” heterogeneous agent models, which depict the real markets more faithfully. We might think of the models proposed by DeLong et al. [18] and their successors as having pre-specified representative agents of two different types, say, a representative rational informed trader and a representative uninformed noise trader. These settings might overlook some important features of financial markets, for example, the interaction and feedback dynamics of traders. In the agent-based approach, we, however, do not assign any agent as being of any specific type exogenously. As a matter of fact, we do not even have the device of representative agents. Hundreds of agents in the model can all have different behavioral rules which they themselves evolve (adapt) over time.4 How many types there are by which they can be distinguished and what these types should be named are difficult issues to be addressed within this highly dynamical evolving environment. However, this is the reality of the real world, isn't it? Finally, in ABSMs, we can also observe what agents (artificial traders) really believe in the depths of their minds when they are trading. This exploration is probably the most striking feature of the agent-based social simulation paradigm. Not only can we observe the macro-phenomena of our artificial society, e.g., the joint dynamics of prices and trading volume, but we can also watch the micro-behavior of every heterogeneous agent down to the details of their thought processes, e.g., the forecasting models or trading strategies that these agents use. Via this feature, we can then trace how the behavior and interaction of agents at the mirco-level can generate macro-level phenomena. Furthermore, we may see whether the agents observing macro-phenomena would change their behavior, and hence may transform the whole financial dynamics into different scenarios (the so-called regime change). These complex feedback relations cannot be well captured by the traditional representative agent model. The rest of the paper is organized as follows: Section 2 describes the ABSM considered in this paper. Section 3 outlines the experimental designs. Section 4 introduces the concept of Granger causality and two different econometric tests used in this paper. Section 5 gives the simulation and testing results both for the “top” and the “bottom”, followed by the concluding remarks in Section 6.

One distinguishing feature of ACE (and thus ABSMs) is that some interesting macro-phenomena of financial markets could emerge (be endogenously generated) from interactions among adaptive agents without exogenously imposing any conditions like unexpected events, information cascades, noise or dumb traders, etc. In this paper, we show that the presence of the stock price–volume causal relation does not require any explicit assumptions like information asymmetry, reaction asymmetry, noise traders, or tax motives. In fact, it suggests that the causal relation may be a generic property in a market modeled as an evolving decentralized system of autonomous interacting agents. We also show that our understanding of the appearance or disappearance of the price–volume relation can never be complete if the feedback relation between individual behavior and aggregate outcome is neglected. This feedback relation is, however, highly complex, and may defy any simple analysis, as in the case of the one we proposed initially. Consequently, econometric analysis which fails to take into account this complex feedback relation between the micro- and macro-aspects may produce misleading results. Unfortunately, we are afraid that this is exactly what mainstream financial econometrics ended up doing in a large number of empirical studies.