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Equilibria in financial markets with heterogeneous agents: A probabilistic perspective
 J. MATH. ECON
, 2004
"... We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and th ..."
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Cited by 29 (3 self)
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We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are “chartist ” or extrapolatory rules. Prices can exhibit transient behaviour when chartists predominate. However, if the probability that an agent will switch to being a “chartist ” is not too high then the process does not explode. There are occasional bubbles but they inevitably burst. In fact, we prove that the limit distribution of the price process exists and is unique. This limit distribution may be thought of as the appropriate equilibrium notion for such markets. A number of characteristics of financial time series can be captured by this sort of model. In particular, the presence of chartists fattens the tails of the stationary distribution.
Timevariation of higher moments in a financial market with heterogeneous agents: An analytical approach, 2003. Working paper
"... A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that so ..."
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Cited by 25 (7 self)
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A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious timeseries characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the interaction among different groups of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman [1993]. Embedding the herding framework into a simple equilibrium asset pricing model, we are able to derive closedform solutions for the timevariation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series. 1
Linking agentbased models and stochastic models of financial markets
 PNAS
, 2012
"... It is wellknown that financial asset returns exhibit fattailed distributions and longterm memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agentbased simulations to understand the unde ..."
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Cited by 16 (3 self)
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It is wellknown that financial asset returns exhibit fattailed distributions and longterm memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agentbased simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agentbased model to quantitatively demonstrate that "fat" tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of longterm memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the longterm memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting. complex systems  power law  scaling laws M odeling price returns has become a central topic in the study of financial markets due to its key role in financial theory and its practical utility. Following models by Engle and Bollerslev (1, 2), many stochastic models have been proposed based on statistical studies of financial data to accurately reproduce price dynamics. In contrast to this stochastic approach, economists and physicists using the tools of statistical mechanics have adopted a bottomup approach to simulate the same macroscopic regularity of price changes, with a focus on the behavior of individual market participants (310). Although the second socalled agentbased approach has provided a qualitative understanding of price mechanisms, it has not yet achieved sufficient quantitative accuracy to be widely accepted by practitioners. Here, we combine the agentbased approach with the stochastic process approach and propose a model based on the empirically proven behavior of individual market participants that quantitatively reproduces fattailed return distributions and longterm memory properties (1114). Empirical and Theoretical Market Behaviors We start by arguing that technical traders (usually agents seeking arbitrage opportunities and make their trading decisions based on price patterns) contribute much more to the dynamics of daily stock prices S t (or log price s t ≡ lnðS t Þ) than fundamentalists (who attempt to determine the fundamental values of stocks). Although fundamentalists hold a majority of the stocks, they trade infrequently (see SI Appendix, Market surveys (1618) also provide clear evidence of the prevalence of technical analysis. We consider here only technical traders, assuming that fundamentalists contribute only to market noise. Our study is of the empirical data recorded prior to 2006 and ignores the effect of high frequency trading (HFT) that has become significant only in the past 5 y. We propose a behavioral agentbased model that is in agreement with the following empirical evidence: i. Random trading decisions made by agents on a daily basis. n 0 technical traders use different trading strategies, hence their decisions to buy, sell, or hold a position appear to be random. A trading decision is made daily because empirical studies report the lack of intraday trading persistence in empirical trading data (19). Market survey (16) also shows that fund managers put very little emphasis on intraday tradings. We estimate the probability p of having daily trade empirically from trading volumes. ii. Price returns. The price return r t ≡ s t − s t−1 is controlled by the imbalance d t between the demand and the supply of stocksthe difference in the number of buy and sell trades each day. The excess in total demand or supply moves the price up or down, where the largest r t occurs when all traders act in unison, when they all either buy or sell their stocks. We assume this relationship between price change r t and d t to be linear each day, as supported by empirical findings (20, 21). iii. Centralized interaction mechanism of returns on technical strategies. For technical traders, an important input parameter in their strategies is past price movement (22, 23). Consequently, prices and orders reflect a main interaction mechanism between agents. In many agentbased models, the interaction strength between agents need to be adjusted with agent population size (5, 24, 25) or interaction structure (26) to sustain "fat" tails in return distributions. Here we propose a centralized interaction mechanism (price change) among agents so that the strength of interaction grows with agent population and is unaffected by interaction structure. iv. Opinion convergence due to price changes. This is the unique mechanism that distinguishes our model from other models. It specifies the collective behavior of technical traders. Duffy et al. (27) found that agents learn from each other and tend to adopt the strategy that gives the most payoff. Given the price patterns at any point in time, a few most profitable technical strategies dominate the market because every technical trader
2002) A minimal noise traders model with realistic time series properties, Symposium of the Society of Nonlinear Dynamics and Econometrics
"... Simulations of agentbased models have shown that the stylized facts (unitroot, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of nonlinearity and interactions, often li ..."
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Simulations of agentbased models have shown that the stylized facts (unitroot, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of nonlinearity and interactions, often limits the analytical approach to the dynamics of these models. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing realistic statistical properties of returns, in close quantitative accordance with the empirical analysis. The simplicity of the system also permits some analytical insights using concepts from statistical mechanics and physics. In our model, the traders are divided into two groups: fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman [22]. The statistical analysis of our simulated data shows longterm dependence in the autocorrelations of squared and absolute returns and hyperbolic decay in the tail of the distribution of the raw returns, both with estimated decay parameters in the same range like empirical data. Theoretical analysis, however, excludes the possibility of ’true ’ scaling
Powerlaw behaviour, heterogeneity, and trend chasing
 J. Econ. Dyn. Control
, 2007
"... Abstract Longrange dependence in volatility is one of the most prominent examples in financial market research involving universal power laws. Its characterization has recently spurred attempts to provide some explanations of the underlying mechanism. This paper contributes to this recent line of ..."
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Abstract Longrange dependence in volatility is one of the most prominent examples in financial market research involving universal power laws. Its characterization has recently spurred attempts to provide some explanations of the underlying mechanism. This paper contributes to this recent line of research by analyzing a simple market fraction asset pricing model with two types of traders fundamentalists who trade on the price deviation from estimated fundamental value and trend followers whose conditional mean and variance of the trend are updated through a geometric learning process. Our analysis shows that agent heterogeneity, riskadjusted trend chasing through the geometric learning process, and the interplay of noisy fundamental and demand processes and the underlying deterministic dynamics can be the source of powerlaw distributed fluctuations. In particular, the noisy demand plays an important role in the generation of insignificant autocorrelations (ACs) on returns, while the significant decaying AC patterns of the absolute returns and squared returns are more influenced by the noisy fundamental process. A statistical analysis based on Monte Carlo Author's personal copy simulations is conducted to characterize the decay rate. Realistic estimates of the powerlaw decay indices and the (FI)GARCH parameters are presented. r
Currency Crisis: Evolution of Beliefs, Experiments with Human Subjects and Real World Data
, 2006
"... We study a model of currency crisis where agents ’ beliefs are the only source of volatility containing the potential for currency devaluation. Using the basic framework of Arifovic and Masson (2003), we examine dynamics generated in two types of agentbased models; one involving social learning, an ..."
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We study a model of currency crisis where agents ’ beliefs are the only source of volatility containing the potential for currency devaluation. Using the basic framework of Arifovic and Masson (2003), we examine dynamics generated in two types of agentbased models; one involving social learning, and another aimed at representing individual learning. As part of our methodology, we conduct a large number of simulations over diverse parameter values in order to verify robustness of the results. As our evaluation methods, we use both experiments with human subjects, and real world data. Our results show that the individual learning model matches the experimental outcomes better than the social learning model. However, we also find that a variant of social learning fits the real world data well. Analysis of our extensive simulations has helped us isolate the elements of our ACE models that influence the dynamics and that can be accounted for the difference between the results in the two types of learning models, as well as between the experimental outcomes and real world data.
AgentBased Modelling of Stock Markets using Existing Order Book Data
 in: Proceedings of 13th International Workshop on MultiAgentBased Simulation (MABS
, 2012
"... Abstract. We propose a new method for creating alternative scenarios for the evolution of a financial time series over short time periods. Using real order book data from the ChiX exchange, along with a number of agents to interact with that data, we create a semisynthetic time series of stock pri ..."
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Abstract. We propose a new method for creating alternative scenarios for the evolution of a financial time series over short time periods. Using real order book data from the ChiX exchange, along with a number of agents to interact with that data, we create a semisynthetic time series of stock prices. We investigate the impact of using both simple, limited intelligence traders, along with a more realistic set of traders. We also test two different hypotheses about how real participants in the market would modify their orders in the alternative scenario created by the model. We run our experiments on 3 different stocks, evaluating a number of financial metrics for intra and interday variability. Our results using realistic traders and relative pricing of real orders were found to outperform other approaches. 1
Network Hierarchy in Kirman’s Ant Model: Fund Investments Can Create Risks∗
, 2008
"... Kirman’s “ant model ” has been used to characterize the expectation formation of financial investors who are prone to herding. In Kirman’s original version, however, the model suffers from the problem of Ndependence: the model’s ability to replicate the statistical features of financial returns van ..."
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Kirman’s “ant model ” has been used to characterize the expectation formation of financial investors who are prone to herding. In Kirman’s original version, however, the model suffers from the problem of Ndependence: the model’s ability to replicate the statistical features of financial returns vanishes once the system size N is increased, and the network structure that describes the feasibility of agent interaction in a generalized version of the ant model determines whether or not the model suffers from Ndependence. We investigate a class of hierarchical networks and find that they do overcome the problem of Ndependence, but at the same time they also increase systemwide volatility, and therefore embody an additional source of volatility besides the behavioral heterogeneity of interacting agents. Interpreting these findings in the context of fund investment, the desire of investors to “play it safe ” might increase systemic risk if coreperiphery networks indeed describe the organizational structure of fund investment. ∗We gratefully acknowledge financial support by the Volkswagen Foundation through
www.ccfea.net Dependence of – and Long Memory in – Exchange Rate Returns: Statistics, Robustness, Time Aggregation ∗
, 2007
"... Empirical research on financial market data reported a number of properties of return time series which are considered as ‘stylized facts’. In this contribution, measures of dependence of foreign exchange rate returns are discussed. Furthermore, statistics of long memory are considered. The robustne ..."
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Empirical research on financial market data reported a number of properties of return time series which are considered as ‘stylized facts’. In this contribution, measures of dependence of foreign exchange rate returns are discussed. Furthermore, statistics of long memory are considered. The robustness of the statistics is analyzed using the bootstrap and considering different subsamples. It is also analyzed how time aggregation affects these properties. Based on the results, robust stylized facts are selected which – together with similar results for unconditional distributions provided in a companion paper – will result in an objective function for an indirect estimation method of agent based models.
www.ccfea.net The Unconditional Distribution of Exchange Rate Returns: Statistics, Robustness, Time Aggregation ∗
, 2006
"... Empirical research on financial market data reports a number of properties of return time series which are considered as ‘stylized facts’. In this contribution, statistics for the unconditional distribution of foreign exchange rate returns are discussed. The robustness of these properties is assesse ..."
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Empirical research on financial market data reports a number of properties of return time series which are considered as ‘stylized facts’. In this contribution, statistics for the unconditional distribution of foreign exchange rate returns are discussed. The robustness of these properties is assessed using the bootstrap and considering different subsamples. The effect of time aggregation is also analyzed. Based on the results robust stylized facts are selected which – together with similar results for conditional distributions and long range dependence provided in a companion paper – will result in an objective function for an indirect estimation method of agent based models.