Stability and bifurcation in a simple heterogeneous asset pricing model

Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. We develop a simple pricing model with two types of rational traders, fundamentalists and chartists, in order to study well price behavior in financial markets, we use student t distribution to replace traditional normal distribution to describe fundamental price process. We study the stability and bifurcation of the underling deterministic system and use numerical simulation to study the dynamic of the stochastic system, including autocorrelations structures and high kurtosis of the returns. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced).     

A simple model of a speculative housing market

We develop a simple model of a speculative housing market in which the demand for houses is influenced by expectations about future housing prices. Guided by empirical evidence, agents rely on extrapolative and regressive forecasting rules to form their expectations. The relative importance of these competing views evolves over time, subject to market circumstances. As it turns out, the dynamics of our model is driven by a two-dimensional nonlinear map which may display irregular boom and bust housing price cycles, as repeatedly observed in many actual markets. Complex interactions between real and speculative forces play a key role in such dynamic developments.     

Asymptotic behavior of market shares for a stochastic growth model

Consider a market with finitely many firms, each enjoying an uncertain growth. We assume the (random) growth rates of these firms are independent and identically distributed. We show that the asymptotic probability distribution of the market shares gives each firm an equal probability of dominating the market (while all other firms are almost extinguished). In particular, these conclusions are independent of the initial market shares of the firms. We conclude that sample paths fluctuate between almost domination and almost extinction. We also demonstrate that these fluctuations may be very slow. Extensions to situations where the total demand is restricted are discussed.     

Existence and uniqueness of stochastic equilibrium in a simple macro model

This paper demonstrates that even the simplest rational expectations macro model may be plagued by nonexistent or multiple equilibria. The reason for these problems is the postulated existence of risk-averse behavior on the part of labor suppliers and purchasers of durable commodities. This risk-averse behavior introduces the price forecast variance into the behavioral parameters of the model, thus leading to a simultaneous nonlinear system.     

A simple model of emerging market portfolio structure

Many emerging market economies have experienced large buildups of foreign exchange rate reserves over the last decade. Much of the contemporary discussion of this phenomenon has focused on this reserve growth as the consequence of exchange rate policies which have maintained fixed pegs to the US dollar. By contrast, this paper focuses on emerging market reserve choice as a consequence of portfolio diversification, applied to the experience of Asian economies. While Asian economies have become significant gross creditors in bonds and other fixed income assets, their liability position in equity and FDI assets has also grown significantly. This suggests that a full understanding of the reserve growth episode must be seen as part of an overall model of portfolio choice. The paper constructs a model of the interaction between an emerging market and an advanced economy in which an optimal general equilibrium portfolio structure implies that emerging market economies simultaneously build up a stock of foreign exchange rate reserves while receiving FDI flows from the advanced economy. The model can provide a reasonable quantitative account of the recent Asian experience.     

Learning rational expectations in an asset market

Will traders in a risky asset market learn Muthian expectations when they initially lack the necessary information? If some traders learn from their observations, will market dynamics depend only on “fundamentals,” as implied by the Efficient Market Hypothesis? This paper shows that at any finite point in time the answer to these questions is “no”. The context is a constant absolute risk aversion model with two kinds of traders and asymmetric information. The market converges asymptotically to a rational expectations equilibrium where prices depend only on fundamentals and the market is efficient.     

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small. Received: April 1, 2000; revised version: January 10, 2001     

Price manipulation in an experimental asset market

We analyze in the laboratory whether an uninformed trader is able to manipulate the price of a financial asset by comparing the results of two experimental treatments. In the benchmark treatment, 12 subjects trade a common value asset that takes either a high or a low value. Only three subjects know the actual value of the asset while the market is open for trading. The manipulation treatment is identical to the benchmark treatment apart from the fact that we introduce a computer program as an additional uninformed trader. This robot buys a fixed number of shares in the beginning of a trading period and sells them again afterwards. Our main result shows that the last contract price is significantly higher in the manipulation treatment if the asset takes a low value and that private information is very well disseminated by both markets if the value of the asset is high. Finally, even though this simple manipulation program loses money on average, it is profitable in some instances.     

Capital asset prices in an oligopolistic market

The author wishes to thank Kalyan Chatterjee, George Monahan, Martin Shubik, and a referee for helpful comments on an earlier version of this paper.     

Portfolio efficiency of a dynamic capital asset pricing model

In the present study we show that, based on equally weighted portfolios of continuously listed Finnish and Swedish stocks, aDynamic Model of Capital Asset Pricing (DCAPM) outperforms the static Capital Asset Pricing Model (CAPM) in the Super Criterion Test. It is demonstrated that the portfolio efficiency of the dynamic model is improved, when using a properly defined transition matrix in the Kalman Filtering Algorithm.The advice and encouragement of Professor Leif Nordberg (Department of Statistics, Åbo Akademi University) is gratefully acknowledged. I thank Jaana Aaltonen for her assistance in monitoring the computer programs. I also thank an anonymous referee for his valuable comments and suggestions for improving the quality of the paper.     

Dynamic sentiment asset pricing model

Conventional wisdom suggests that the equilibrium stock price is not affected by investor sentiment, and the equilibrium price at an early time is higher than the one at a later time. In contrast to this wisdom, we present a dynamic asset pricing model with investor sentiment and we find that investor sentiment has a significant impact on the equilibrium stock price. The equilibrium stock price, which is affected by pessimistic sentiment at time 0, may be lower than the one at time 1. Moreover, consistent with the reality stock market, our model shows that time varying sentiments can lead to various price changes. Finally, the model could offer a partial explanation for the financial anomaly of high volatility.     

A general asset pricing model

With only minimal assumptions, a general version of the security market line is obtained. In addition, it is suggested that instead of concentrating on the relationship between risk and return, the testable theories of capital market equilibrium should contain specific hypotheses about the true aggregate demands and supplies of risky assets.     

Career concerns in a simple experimental labour market

We experimentally investigate a simple version of Holmström's career concerns model in which firms compete for agents in two consecutive periods. Profits of firms are determined by agents’ unknown ability and the effort they choose. Before making second-period wage offers firms are informed about first-period profits. In a different treatment firms additionally learn the abilities of agents. Theory suggests high first-period equilibrium effort in the hidden ability treatment but no effort elsewhere. However, we find that effort tends to be higher in the revealed ability treatment and therefore conclude that transparency does not weaken, but strengthen career concerns incentives.     

Internal rationality, imperfect market knowledge and asset prices

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are ‘internally rational’, i.e., maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future, but agents may not be ‘externally rational’, i.e., may not know the true stochastic process for payoff relevant variables beyond their control. This includes future market outcomes and fundamentals. We apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors? expectations of the price and dividend in the next period, rather than by expectations of the discounted sum of dividends. As a result, learning about price behavior affects market outcomes, while learning about the discounted sum of dividends is irrelevant for equilibrium prices. Stock prices equal the discounted sum of dividends only after making very strong assumptions about agents? market knowledge.     

International asset market, nonconvergence, and endogenous fluctuations

We develop an overlapping generations model with re-tradeable paper assets and capital accumulation to analyze the interaction between the real economy and an international asset market. The world consists of two homogeneous countries, which differ only in their initial levels of capital. Consumers who live for two periods transfer wealth over time and across countries by holding international mutual funds which pay stochastic dividends. The optimal portfolio decisions of consumers do not necessarily induce convergence of incomes between the two countries. Moreover, interaction through the asset market induces endogenous fluctuation of capital flows between the rich and the poor country.     

A direct test of hyperbolic discounting using market asset data

This paper introduces a framework that generalizes exponential discounting in a net present value model by including a quasi-hyperbolic discount parameter in the asset valuation equation. Using observed market asset data, a statistically significant quasi-hyperbolic parameter is obtained, thus rejecting exponential discounting.     

Labour market implications of EU product market integration

European labour markets are in a state of flux due to the changing market situation induced by international integration. This process affects wage formation through more fierce product market competition and increased mobility of jobs. This development is by some observers taken to enforce labour market flexibility, while for others it signals an erosion of social standards and in turn possibly the welfare society. Since labour is not very mobile in Europe, the effects of international integration on labour markets are mostly indirect via product market integration. We review the channels through which product market integration affects labour markets and perform an empirical analysis of the convergence and interdependencies in wage formation among EU countries. We find that integration is changing labour market structures and inducing wage convergences as well as stronger wage interdependencies, but it is a gradual process. Moreover, the present study does not support the view that international integration will lead to a 'race to the bottom' and rapidly erode domestic labour markets standards, nor that it will relieve politicians of the need to consider labour market reforms to improve labour market performance.     

Policy implications of a non-linear Phillips curve in a stochastic environment

When the Phillips curve is non-linear, fluctuations of the unemployment rate below the mean will have a larger impact on the inflation rate than fluctuations above the mean. This paper shows that this causes conventional measures of the “natural unemployment rate” to underestimate the mean unemployment rate consistent with stable inflation in the long run. More importantly, it reveals a potential long-run trade-off between unemployment and economic stability.     

The asymptotic shapley value for a simple market game

We consider the game in which b buyers each seek to purchase 1 unit of an indivisible good from s sellers, each of whom has k units to sell. The good is worth 0 to each seller and 1 to each buyer. Using the central limit theorem, and implicitly convergence to tied down Brownian motion, we find a closed form solution for the limiting Shapley value as s and b increase without bound. This asymptotic value depends upon the seller size k, the limiting ratio b/ks of buyers to items for sale, and the limiting ratio of the excess supply relative to the square root of the number of market participants. This work was sponsered in part by NSF Grant DMS-03-01795.     

Pareto improving price regulation when the asset market is incomplete

Summary. Incomplete asset markets cause competitive equilibria to be constrained suboptimal and provides scope for Pareto improving interventions. In this paper, we examine how intervention in prices in asset or spot commodity markets serves this purpose. We show that, if fix-price equilibria behave sufficiently regularly near Walrasian equilibria, Pareto improving price regulation is generically possible. An advantage of price regulation, contrasted with interventions in individuals asset portfolios, is that it operates anonymously, on market variables.Received: 12 August 2002, Revised: 10 July 2003, JEL Classification Numbers: D45, D52, D60.Earlier and longer versions were circulated as Discussion Paper No. 9841 (June, 1998), CORE, Université Catholique de Louvain, and Working Paper No. 01-31 (2001), Department of Economics, Brown University.The research of Herings was made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organization for Scientific Research (NWO); while this paper was being written, he enjoyed the generous hospitality of the Cowles Foundation.John Geanakoplos and Hamid Sabourian asked questions that clarified a number of points in earlier drafts of the paper. An anonymous referee made comments that were insightful and helpful.