Endogenous fluctuations in a simple asset pricing model with heterogeneous agents

Abstract In this paper we study the adaptive rational equilibrium dynamics in a simple asset pricing model introduced by Brock and Hommes (System Dynamics in Economic and Financial Models, Wiley, Chichester, 1997, pp. 3–44; Journal of Economic Dynamics and Control, 22, 1998, 1235–1274). Traders have heterogeneous expectations concerning future prices and update their beliefs according to a risk adjusted performance measure and to market conditions. Further, also their expectations about conditional variances of returns vary over time. We show that even for the simple case where agents can only choose between two different predictors complicated dynamics arise and we analyse the bifurcation routes to chaos.

[1]  Willaiam A. Brock,et al.  Asset Price Behavior in Complex Environments , 1996 .

[2]  Mordecai Kurz,et al.  Endogenous economic fluctuations : studies in the theory of rational beliefs , 1997 .

[3]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[4]  A. Robert,et al.  HAUGEN, . The New Finance: The Case against Efficient Markets (Englewood Prentice Hall. , 1995 .

[5]  Jean-Michel Grandmont,et al.  Expectations formation and stability of large socioeconomic systems , 1998 .

[6]  T. Lux.  Herd Behaviour, Bubbles and Crashes , 1995 .

[7]  S. Smale.  Diffeomorphisms with Many Periodic Points , 1965 .

[8]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[9]  Daniel B. Nelson,et al.  Filtering and Forecasting with Misspecified Arch Models Ii: Making the Right Forecast with the Wrong Model , 1992 .

[10]  L. Blume,et al.  Evolution and market behavior , 1992 .

[11]  M. Goldman,et al.  On the Dynamic Behavior of Prices in Disequilibrium , 1980 .

[12]  Gerhard Sorger,et al.  CONSISTENT EXPECTATIONS EQUILIBRIA , 1998, Macroeconomic Dynamics.

[13]  Rajiv Sethi,et al.  Cautious trend-seeking and complex asset price dynamics , 1998 .

[14]  Dean P. Foster,et al.  Filtering and Forecasting with Misspecified Arch Models Ii: Making the Right Forecast with the Wrong Model , 1992 .

[15]  Blake LeBaron.  Experiments in Evolutionary Finance , 1995 .

[16]  Douglas M. Patterson,et al.  Nonlinear Dynamics, Chaos, And Instability , 1994 .

[17]  Andrei Shleifer.  Positive Feedback Investment Strategies , 2000 .

[18]  W. Brock.  PATHWAYS TO RANDOMNESS IN THE ECONOMY , 1993 .

[19]  C. Praagman,et al.  System Dynamics in Economic and Financial Models , 1997 .

[20]  V. Nikolaev,et al.  Physical and Biological Modification of Carbonic Sorbents , 1992 .

[21]  William A. Brock,et al.  A rational route to randomness , 1997 .

[22]  R. Thaler.  Advances in behavioral finance , 1995 .

[23]  T. Sargent.  Bounded rationality in macroeconomics , 1993 .

[24]  Kenneth A. Froot,et al.  Chartists, Fundamentalists and the Demand for Dollars , 1991 .

[25]  André de Palma,et al.  Discrete Choice Theory of Product Differentiation , 1995 .

[26]  Carl Chiarella,et al.  The dynamics of speculative behaviour , 1992, Ann. Oper. Res..

[27]  R. Palmer,et al.  Asset Pricing Under Endogenous Expectations in an Artificial Stock Market , 1996 .

[28]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[29]  H. Tong.  13. Chaotic Dynamics: Theory and Applications to Economics , 1996 .

[30]  Markus K. Brunnermeier.  Prices, Price Processes, Volume and Their Information - A Survey of the Market Microstructure Literature - , 1998 .

[31]  C. Leake.  Discrete Choice Theory of Product Differentiation , 1995 .

[32]  Blake LeBaron,et al.  A Dynamic Structural Model for Stock Return Volatility and Trading Volume , 1995 .

[33]  Rajiv Sethi,et al.  Endogenous regime switching in speculative markets , 1996 .

[34]  Thanasis Stengos,et al.  Technical Trading Rules and the Size of the Risk Premium in Security Returns , 1997 .

[35]  B. LeBaron,et al.  Simple Technical Trading Rules and the Stochastic Properties of Stock Returns , 1992 .

[36]  L. Summers,et al.  Positive Feedback Investment Strategies and Destabilizing Rational Speculation , 1989 .

[37]  R. Palmer,et al.  Time series properties of an artificial stock market , 1999 .

[38]  C. M. Place,et al.  An Introduction to Dynamical Systems , 1990 .

[39]  E. Barucci,et al.  The Rise of Complex Beliefs Dynamics , 1996 .

[40]  Floris Takens,et al.  Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors , 1993 .

[41]  L. Ghezzi.  Bifurcations in a stock market model , 1992 .

[42]  Sanford J. Grossman.  The Informational Role of Prices , 1990 .

[43]  M. Marchesi,et al.  VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS , 1998 .

[44]  L. Summers,et al.  The Noise Trader Approach to Finance , 1990 .

[45]  Richard H. Day,et al.  Bulls, bears and market sheep , 1990 .

[46]  W. Brock,et al.  Heterogeneous beliefs and routes to chaos in a simple asset pricing model , 1998 .

[47]  J. Goeree,et al.  Heterogeneous beliefs and the non-linear cobweb model , 2000 .

[48]  R. Thaler.  Quasi Rational Economics , 1991 .

[49]  L. Summers,et al.  Noise Trader Risk in Financial Markets , 1990, Journal of Political Economy.

[50]  Marcelo Viana,et al.  Strange attractors in higher dimensions , 1993 .

[51]  Robert A. Haugen.  Beast on Wall Street: How Stock Volatility Devours Our Wealth , 1998 .

[52]  William A. Brock,et al.  Models of complexity in economics and finance , 1997 .