بررسی اثر محدودیت های قیمت در بازار سهام مصنوعی

This paper proposes an agent-based framework to examine the effectiveness of price limits in an artificial stock market. The market is composed of many boundedly rational and heterogeneous traders whose learning behavior is represented by a genetic programming algorithm. We calibrate the model to replicate several stylized facts observed in real financial markets. Based on this environment, the impacts of price limits are analyzed from the perspectives of volatility, price distortion, volume, and welfare. We find that the imposition of price limits possesses both positive and negative effects. However, compared with the market without price limits, appropriate price limits help to reduce volatility and price distortion, and increase the liquidity and welfare.

The efficient market hypothesis (EMH) (Fama, 1970) is one of the cornerstones of financial economics. Basically, the EMH requires that, on average, traders behave rationally and have rational expectations. It asserts that asset prices fully reflect all available information and always reflect their intrinsic value. In this situation, future price movements cannot be predicted on the basis of past information. Any financial regulation imposed on the market should generate no substantial effects but may result in delayed revelation of the information. Examining the efficiency of real financial markets has thus been an interesting topic over the past three decades. Many studies have questioned the validity of the EMH in real financial markets and provide the theoretical foundations or empirical evidence to show the existence of market inefficiency. De Long et al. (1991) point out that noise traders may survive in the long run and exert their impact on price dynamics. Kogan et al. (2006) further indicate that irrational traders can persistently maintain a large impact even though their relative wealth becomes quite small. Lo and MacKinlay (1988), Campbell and Shiller (1988), Brock et al. (1992), and Neely et al. (1997) all find evidence of predictability and profitability in financial markets. In addition, financial markets usually experience high volatility, and bubbles and crashes never cease. This phenomenon cannot be purely explained by the changes in fundamentals. The question that naturally arises is whether there exist ways to effectively regulate financial markets. The financial market crashes that took place in 1987 gave rise to much debate regarding how to prevent the markets from experiencing such large fluctuations. Recommendations that circuit breakers such as price limits and trading halts be implemented were some of the outcomes. Price limits and trading halts work in different ways. They differ in that trading is only permissible within the pre-specified daily price variation range in the former case, while the latter results in the suspension of the trading process once the asset prices reach the pre-specified boundaries. After some pre-determined time duration, the market is reopened and new boundaries of prices are provided. The main purpose behind imposing price limits is to reduce price volatility by repressing excessive speculation and mob psychology. The rationale for supporting price limits is referred to as the overreaction hypothesis. Proponents assert that traders are prone to overreacting to new information, so that asset prices may deviate from their fundamental values. The empirical evidence from cognitive psychology also supports this argument, e.g. Tversky and Kahneman (1974). It is believed that price limits may provide a cooling-off period for traders to reassess the intrinsic asset value. Volatility is then reduced. The empirical results obtained in Ma et al. (1989) and Lee and Kim (1995) are consistent with the overreaction hypothesis. By contrast, opponents of price limits who support the information hypothesis, e.g. Fama (1989), Chen (1998), and Kim and Rhee (1997), argue that traders in financial markets are able to process information efficiently. The imposition of price limits may generate negative effects such as delayed price discovery, volatility spillover, and trading interference. Although many papers have focused on examining the effectiveness of price limits,1 a consensus in terms of opinion has so far not been reached. From a theoretical point of view, the results may present different pictures based on different assumptions or frameworks (Brennan, 1986, Kodres and O’Brien, 1994, Chowdhry and Nanda, 1998 and Chou et al., 2000). In addition, such debates mainly result from the different assumptions regarding rationality that the researchers adopt to characterize market traders. People who advocate the imposition of price limits presume that traders are generally irrational in the sense that they use wrong beliefs. However, this contention overlooks the fact that traders, even though they are irrational, may adapt to and learn how to react to the market environment. As time goes by, they may behave rationally in that they perceive the fundamental values of the asset, and the negative impacts of the imposition of price limits then emerges. By contrast, those who disagree with the usefulness of price limits assume that traders are rational. Being completely rational means either that traders inherently perceive the intrinsic values of the asset, or that traders have tremendous computational abilities that make them correctly respond to any change in market conditions. However, such reasoning has been questioned by many empirical results. Simon (1957) and Tversky and Kahneman (1974) argue that humans do not behave rationally. Examining the effectiveness of price limits based on empirical data also poses great difficulties. First, it may suffer from econometric (Chou, 1997) or data-acquisition problems. Second, the rationality at the top, i.e. from the perspective of market phenomena, is not necessarily consistent with that at the bottom, i.e. traders’ rationality. Gode and Sunder (1993) find that the market's rationality could result from the individuals’ irrationality. Third, empirically discriminating between the information hypothesis and the overreaction hypothesis would be problematic, when neither understanding what had been on the traders’ minds nor being able to predict what would have happened had the price limits not been imposed. Actually, a similar concept has been mentioned in Harris (1998): Without mind-reading techniques and without reliable methods for reconstructing a false history, one cannot reliably discriminate between the two perspectives. (p. 34) To resolve these problems, a simulated financial market composed of many interacting, heterogeneous, and boundedly rational traders whose learning behavior is appropriately represented, together with an environment without exogenous shocks, seems to be a more reasonable framework. In such a framework, the interaction between the traders themselves and that between traders and market regulations could be well examined. Moreover, a pure environment which can serve as the objective benchmark is obtainable, so that we would be able to answer how the market would behave if current rules on price limits faced a different situation. The studies on financial markets based on the heterogeneous agent model (HAM) have grown quite rapidly in the past decade since traditional arguments regarding traders’ rationality have been challenged. Simon (1957) argues that bounded rationality is a more acceptable concept for describing a human's behavior. Besides, financial data usually exhibit several stylized facts such as volatility clustering and fat tails for the return series, as well as volume persistence of which the causes cannot be well-explained by traditional asset pricing models. Kirman (2006) points out that heterogeneity is an essential part of the evolutionary system, and heterogeneous and varying expectations may account for many of the stylized facts. Many heterogeneous agent models have been proposed to generate rich and complicated market dynamics, and they successfully mimic the stylized facts observed in financial markets and provide explanations regarding some of these phenomena.2 The advantages of heterogeneous agent models of financial markets are addressed in Hommes (2006) and LeBaron (2006), who also provide an extensive review of this research area. Hommes (2006) pays more attention to the simple, stylized versions where there exist only a few different types of traders, so that analytical solutions are obtainable, while LeBaron (2006) largely discusses the models with many different types of traders where theoretical results are difficult to derive. Therefore, the papers reviewed in LeBaron (2006) heavily rely on computational methods. There is no doubt that traders are heterogeneous in many dimensions for they may possess heterogeneous beliefs, endowments, or attitudes toward risk aversion. In addition, they adopt certain kinds of adaptive learning methods to explore underlying regularities for making decisions based on incomplete and/or imperfect information. Once we take these factors into account, agent-based models employing computational tools to study the dynamic processes of many interacting and heterogeneous agents will be more appropriate. As long as the agent-based models are appropriately calibrated based on empirical validation as well as behavioral motifs, the agent-based approach will be able to not only provide explanations of economic or financial puzzles but will also serve as the test bed for the discovery and understanding of good institutional designs.3 The goal of this paper is to provide an agent-based artificial financial market to examine the effectiveness of price limits. To the best of our knowledge, Westerhoff (2003), who proposed a chartist-fundamentalist model, was the first to examine the effectiveness of price limits based on the agent-based modeling approach. Westerhoff (2003) finds that price limits can reduce volatility and make prices less distorted, while the price distortion may increase if price limits are too restrictive. Such results have recently been confirmed by Westerhoff, 2006 and Westerhoff, 2008 where different settings in relation to fundamental or technical trading rules are employed. The remarkable work of Westerhoff, 2003, Westerhoff, 2006 and Westerhoff, 2008 does provide a novel track to reexamine the effects of price limits. However, several designs seem to be inappropriate in a general environment. First, like many other agent-based models which include Chiarella (1992), Brock and Hommes (1998), and LeBaron et al. (1999), assuming that traders rely on a set of trading rules of pre-specified forms may restrict the traders’ ability to process information and possibly result in biased outcomes. In the absence of the evolution of the trading strategies, the heterogeneity of the traders’ beliefs, the momentum for the profound financial phenomena, is then restrained. Kirman (2006) and LeBaron (2006) also point out the importance of such characteristics. Second, the traders are all assumed to perceive the fundamental values of the asset. This assumption is mainly demanded by the widely used chartist-fundamentalist approach to distinguish the trading rules adopted by the fundamentalists from those adopted by the chartists, while in general there is no reason to assume that traders are aware of these fundamental values and that they would respond accordingly. To avoid such criticisms, we propose an artificial stock market model which is closely related to the framework of Brock and Hommes (1998) and the Santa Fe Artificial Stock Market (SF-ASM) of Arthur et al. (1997) and LeBaron et al. (1999). The modeling techniques used for traders’ expectations and the market mechanism are, however, different. Genetic programming (GP) serves as the modeling tool for traders’ expectations with the double auction (DA) approach being used as the trading system. Since GP is able to represent hierarchical strategies of different sizes and shapes, this seems to be a more appropriate representation.4 Besides the formation of traders’ expectations, the trading mechanism is also an important concern. The DA is the principal trading system for most financial markets around the world. Therefore, compared to previous studies, our framework may reveal more interesting and valuable features. The remainder of this paper is organized as follows. Section 2 describes the basic framework of the artificial stock market, the traders’ characteristics, and the mechanism of price determination. The model's calibration and the simulation design are presented in Section 3. Section 4 shows the simulation results and examines the effectiveness of the price limits. Section 5 concludes.

This paper examines the effectiveness of price limits under the framework of bounded rationality and agent-based modeling. We find that price limits have both positive and negative effects on the market. On the positive side, under appropriate price limit levels, volatility and distortion are reduced, and liquidity is improved. The main reasons for this are as follows. In reality, traders are characterized by bounded rationality. They are unaware of the intrinsic value of the asset. The available information that traders can use to infer the fundamental value of the asset is usually insufficient or imperfect. Traders then modify their forecasts on the basis of current information in that the anchoring effect comes into play. This part has been overlooked by the people who opposed the price limit rules. In addition, Kodres and O’Brien (1994) mention that market imperfections may be the reason why circuit breakers will be positive. One of the market imperfections is the market's limited capacity to absorb massive one-sided shocks. Therefore, it is not surprising that the imposition of price limits has substantial and positive impacts such as lower market volatility and price distortion, and higher welfare. However, price limits also generate negative effects on the market, i.e. they distort traders’ expectations and inhibit traders’ abilities in figuring out the intrinsic value of the stock. Under inappropriate ranges of price limits, the negative impact may overwhelm the positive. The question that remains is how to select appropriate price limits to achieve the policy goal. The decision should be made after taking into consideration the need to maintain a balance between the market instability and the distortion regarding traders’ expectations. Besides, the impact of price limits on market liquidity exhibits a non-monotonic feature, so that policy-makers should consider how a change in price limits affects traders’ heterogeneity in expectations and also take the bid-ask spread into account. Of course, our results are closely related to the way in which the traders’ behavior is modeled, which is quite important in the framework of bounded rationality. Therefore, it is very normal to ask whether these results will change under different modelings of traders’ rationality. This, however, is left to future research.