Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions.     

Arbitrage and price revelation with asymmetric information and incomplete markets

This paper deals with the issue of arbitrage with differential information and incomplete financial markets, with a focus on information that no-arbitrage asset prices can reveal. Time and uncertainty are represented by two periods and a finite set S of states of nature, one of which will prevail at the second period. Agents may operate limited financial transfers across periods and states via finitely many nominal assets. Each agent i has a private information about which state will prevail at the second period; this information is represented by a subset S_i of S. Agents receive no wrong information in the sense that the “true state” belongs to the “pooled information” set ∩_iS_i, hence assumed to be non-empty.Our analysis is two-fold. We first extend the classical symmetric information analysis to the asymmetric setting, via a concept of no-arbitrage price. Second, we study how such no-arbitrage prices convey information to agents in a decentralized way. The main difference between the symmetric and the asymmetric settings stems from the fact that a classical no-arbitrage asset price (common to every agent) always exists in the first case, but no longer in the asymmetric one, thus allowing arbitrage opportunities. This is the main reason why agents may need to refine their information up to an information structure which precludes arbitrage.     

Multiproduct price competition with heterogeneous consumers and nonconvex costs

This paper extends the oligopolistic model of price competition to environments with multiple goods, heterogeneous consumers, and arbitrary continuous cost functions. A Nash equilibrium in mixed strategies with an endogenous sharing rule is proven to exist. It is also shown that, in environments with fixed costs and constant marginal costs, all (symmetric and asymmetric) equilibria exhibit price dispersion across stores. Furthermore, the paper identifies scenarios in which prices will necessarily be random. In these markets, stores keep each other guessing because, given the fixed costs, they would incur a loss if their price strategies were anticipated and beaten by competitors. This is interpreted as an important economic feature that is possibly behind random price promotions such as weekly specials.     

Volatility of exchange rate futures and high-low price spreads

This study explores the time-series behavior and the predictability of daily percentage changes in the Japanese Yen futures contracts. The relationship between currency futures volatility and high-low price spreads in the Japanese Yen futures contracts is examined. In addition, this study explores the issue of first- and second-order dependencies in the Japanese Yen futures contract prices changes, address the issue of asymmetric volatility, and examine the extent to which the information contained in the high-low price spreads can be used to predict future Japanese Yen currency futures contract price changes. The analysis is carried out using the EGARCH model. The volatility of the Japanese Yen currency futures price changes is adequately modeled by an EGARCH process and is predictable using information contained in the high-low price spread variables constructed in this study. This study also finds a positive and significant relationship between the spread variable and the conditional mean of price changes, suggesting that current information contained in the spread variable can be used to predict future Japanese Yen currency futures contract price changes. The hypothesis that volatility is an asymmetric function of past innovations is confirmed.     

Asset price dynamics with heterogeneous beliefs and local network interactions

In this paper we investigate the effects of network topologies on asset price dynamics. We introduce network communications into a simple asset pricing model with heterogeneous beliefs. The agents may switch between several belief types according to their performance. The performance information is available to the agents only locally through their own experience and the experience of other agents directly connected to them. We model the communications with four commonly considered network topologies: a fully connected network, a regular lattice, a small world, and a random graph. The results show that the network topologies influence asset price dynamics in terms of the regions of stability, amplitudes of fluctuations and statistical properties.     

Intra-day futures price volatility: Information effects and variance persistence

This paper was prepared for presentation at the Conference on Nonlinear Dynamics and Econometrics, UCLA, 5–6 April, 1991, under the title ‘Information and chronological time effects in intra-day futures price volatility.’ The authors are grateful to participants of the Nonlinear Dynamics Conference and to Leigh Riddick, George Wang, and two anonymous referees for helpful comments. The BDS program was provided by W. D. Dechert and the BISPEC program was provided by Doug Patterson. The views stated within are those of the authors, and do not necessarily reflect those of the Commodity Futures Trading Commission or its staff. This paper examines the role of the rate of information arrival proxy variables, as they relate to persistence in the variance structure of minute-by-minute S&P 500 Index Futures returns series. The role of contract volume, floor transactions, the number of price changes, executed order imbalance, and an information composite in reducing variance persistence is examined. All proxy variables are found to explain a significant amount of returns variance. While the characteristics of returns data vary daily, some evidence of remaining variance persistence is found, regardless of the definition of the rate of information arrival variable. Our results suggest that utilization of a pure ARCH-type model for highfrequency returns data implies a mis-specification.     

Preemptive behavior in sequential-move tournaments with heterogeneous agents

Rank-order tournaments are usually modeled simultaneously. However, real tournaments are often sequential. We show that agents' strategic behavior in sequential-move tournaments significantly differ from the one in simultaneous-move tournaments: In a sequential-move tournament with heterogeneous agents, the first acting agent may choose a preemptively high effort so that the following agent gives up. The principal is able to prevent preemptive behavior in equilibrium by choosing a sufficiently small spread between winner and loser prize. Received: January 2003, Accepted: November 2004 JEL Classification: J3, M12, M5 We would like to thank two anonymous referees and the editor Kai Konrad for helpful comments. Financial support by the Deutsche Forschungsgemeinschaft (DFG), projects no. KR 2077/2-1 and SFB/TR 15 ("Governance and the Efficiency of Economic Systems"), is gratefully acknowledged.     

States of psychological anchors and price behavior of Japanese yen futures

This study explores whether the relationship between Japanese yen futures returns and the corresponding equity returns is affected by the states of psychological anchors of the currency and stock markets. This study employs the linear-regression-based tree model (a machine learning method) to account for the framing effect of the anchors. The empirical results of the linear-regression-based tree model show that the currency price behaviors of momentum and reversal, and prediction by equity markets, vary with the anchors. Empirical evidence also indicates that the linear-regression-based tree model outperforms the OLS model based on the estimation results and out-of-sample forecasting. The forecasting performance of the linear-regression-based tree model can be improved along with an increase in the forecasting period.     

Arbitrage, strategic inefficiency and self-regulation

This paper develops a multi-period strategic market game in two different settings, one of a finite-period finance economy, and its extension to infinite periods but with overlapping term of traders. Under these two different contexts, we address the possibility of strategies that Pareto improve the outcome of the game. In this effort, both the introduction of a regulation scheme and the innovative role of provision of traders with incentives to self-police these designated strategies play an important role.     

Index futures trading and stock price volatility: Evidence from Denmark and France

This study uses an EGARCH methodology to investigate the impact of index futures trading on the price volatility of two European stock markets. The results show that index futures trading has changed the distribution of stock returns in Denmark and France, however, it has not increased stock price volatility. There is evidence that futures trading has dampened stock price fluctuations in France. The results further show that stocks in Denmark and France exhibit strong volatility persistence and asymmetry, especially during the post-futures period.     

A heterogeneous agent model of asset price dynamics with two time delays

This study constructs a heterogeneous agents model of a financial market in a continuous-time framework. There are two types of agents, fundamentalists and chartists. The former follows the traditional efficiency market theory and has a linear demand function, whereas the latter experiences delays in the formation of price trends and possesses a S-shaped demand function. The main feature of this study is a theoretical investigation on the effects caused by two time delays in a price adjustment process. In particular, two main results are demonstrated: One is that the stability switching curves are analytically derived, and the other is that the stability losses and gains can repeatedly occur when the shape of the curves are meandering. Although it is well known that a time delay has a destabilizing effect, these results imply that multiple delays can stabilize and destabilize a market price generating persistent deviations from the stationary price.     

Innovation diffusion with heterogeneous networked agents: a computational model

It is well established that S-shaped curves describe the diffusion processes of many innovations quite well, but little insight on the mechanics of diffusion is achieved by simple curve fitting. We propose an evolutionary model of the diffusion process, focusing on the characteristics of economic agents and on the interactions among them, and relate those determinants with the observed shape of the diffusion curve. Using simulation techniques, we show that the proposed model is able to explain why an innovation may not diffuse globally across an economy/region, even when it faces no rival innovations. Moreover, we show how network size, informational spillovers, and the behavior of innovation prices shape the diffusion process. The results regarding network size and informational spillovers rationalize the importance of informational lock-outs, proving they can influence both the aggregate adoption rate and the speed of the diffusion process. With respect to innovation prices, simulation results show that faster price decline leads to higher aggregate adoption rates, and that the diffusion process is more sensitive to the pricing dynamics than to the network size or the behavior of spillovers.     

The existence of rational expectations equilibria in a large economy with noisy price observations

Non-revealing rational expectations equilibria exist in microeconomic pure exchange economies in which a continuum of uninformed agents have suitably distributed noisy price observations. Slight dispersion in the prices observed by the subset of uninformed consumers is the key condition for continuity (and smoothness) of aggregate excess demand, although individual demands are discontinuous. It leads to equilibria in which markets approximately clear in a strong sense. The equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions.     

Ex-post rational price approximations and the empirical reliability of the present-value relation

Excess volatility and regression tests have resulted in apparent rejections of the present-value relation when ex-post price approximations are employed. These approximations are based upon a sample terminal condition for prices, are not ergodic time-series, and do not result in statistics with readily calculable standard errors. Kleidon (1986a) has demonstrated that ex-post price approximations can subtly affect the reliability of certain volatility tests. We use a bootstrapped cointegration model to demonstrate some of these same effects in Mankiw, Romer and Shapiro's (1985) volatility statistics. The volatility statistics rarely have positive expected value in finite samples and still do not reject the presentvalue relation. Approximations based upon a ‘rolling’ terminal condition result in volatility statistics which have calculable large-sample errors, but even these standard errors greatly overstate the accuracy of volatility statisics in small samples. Regression tests of the present value relation are also affected by the price approximations.     

Optimal money growth in a limited participation model with heterogeneous agents

This paper studies optimal money growth in a cash-in-advance production economy with heterogeneity in patience levels and know-how. We show that the rate of deflation suggested by the Friedman rule is limited by the subjective discount rate of the most patient agent in the economy. The output distortion due to cash-in-advance constraints on firms can completely be eliminated by means of the Friedman rule if and only if firms are run by the most patient agents.Received: 16 August 2003, Accepted: 22 March 2005, JEL Classification: D52, D90, E21, E41, E52Parts of this paper were completed while the first and second authors were visiting the University of York and Princeton University respectively. We are thankful for the hospitality of these institutions. The second author also acknowledges the hospitality and support of Bilkent University that he is currently visiting, the support from the Turkish Academy of Sciences in the framework of the ‘Distinguished Young Scientist Award Program’ (TUBA-GEBIP/2004), the grant awarded by the Scientific and Technical Research Council of Turkey (TUBITAK) under the NATO Science Fellowship Program as well as the support from the Center for Economic Design of Bogaziçi University. This paper was presented in the ERC/METU Second International Conference on Economics, Ankara, September 1998, and at seminars in Bilkent, Bogaziçi and Ohio State Universities. We thank, in particular, Emre Alper, Sumru Altug, Huw Dixon, Tatsuro Ichiishi, Ivan Pastine, Murat Sertel and Alan Sutherland for useful comments. We also thank two anonymous referees for comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily reflect that of the Central Bank of Republic of Turkey.     

Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty

This paper describes the first model considered in the computational suite project that compares different numerical algorithms. It is an incomplete markets economy with a continuum of agents and an inequality (borrowing) constraint.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Growth,speculation and sprawl in a monocentric city

An economic theory of sprawl in a growing, monocentric city is presented. Where decision-makers have perfect foresight, leapfrog development and discontinuous land-rent functions may occur and be efficient in both an ex post and ex ante sense. Where the extent of future growth is uncertain, decision-makers become speculators and the spatial pattern of development is more complicated. Ex post inefficiency generally occurs.