New models of trader beliefs and their application for explaining financial bubbles

One challenging and exigent problem in behavior finance is how to establish verifiable models describing the appearance and burst of price bubbles. Current results are enhanced in this paper through a series of improvement as follows: new models are proposed for describing the return and dividend processes, especially the trader's behavior with the adaptive expectation belief and the bounded rational expectation belief, respectively; with these models, we establish dynamical systems in terms of the price-to-earnings ratio and the forecast-to-earnings ratio; the detailed solution and asymptotic analysis of these equations provide new, elaborate and quantitative explanations for both the formation and disappearance of different price bubbles; inspired by the herd behavior framework, a new random belief evolutionary mechanism is devised to model the belief change between two beliefs; a specific genetic algorithm is designed to efficiently estimate model parameters; simulation and empirical studies are carried out to illustrate the application of new methods. Both theoretical and empirical results sufficiently show the reasonability, practicality, efficiency and robustness of our new models and methods for properly explaining the appearance and burst of different kinds of price bubbles.

[1]  Didier Sornette,et al.  Critical Market Crashes , 2003, cond-mat/0301543.

[2]  I. Gabitov,et al.  Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles , 2000 .

[3]  Shintaro Nakao,et al.  On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations , 1972 .

[4]  Cars Hommes,et al.  Expectations and Bubbles in Asset Pricing Experiments , 2008 .

[5]  R. Shiller,et al.  Stock Prices, Earnings and Expected Dividends , 1988 .

[6]  J. Muth Rational Expectations and the Theory of Price Movements , 1961 .

[7]  European Business Fluctuations in the Austrian Framework , 2008 .

[8]  Sebastiano Manzan,et al.  Behavioral Heterogeneity in Stock Prices , 2005 .

[9]  C. Hommes Heterogeneous Agent Models in Economics and Finance , 2005 .

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

[11]  G. Chow,et al.  Rational Versus Adaptive Expectations In Present Value Models , 1989 .

[12]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[13]  B. LeBaron Agent-based Computational Finance , 2006 .

[14]  A. Krawiecki,et al.  Stochastic resonance as a model for financial market crashes and bubbles , 2003 .

[15]  N. Gertchev A Critique of Adaptive and Rational Expectations , 2007 .

[16]  Extracting the exponential behaviors in the market data , 2006, physics/0608008.

[17]  Florian Wagener,et al.  Complex Evolutionary Systems in Behavioral Finance , 2008 .

[18]  The Dynamics of Trader Motivations in Asset Bubbles , 2005 .

[19]  G. McLachlan Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[20]  Mark P. Taylor,et al.  The use of technical analysis in the foreign exchange market , 1992 .

[21]  D. Sornette,et al.  Large financial crashes , 1997, cond-mat/9704127.

[22]  Leigh Tesfatsion,et al.  Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics (Handbook of Computational Economics) , 2006 .

[23]  D. Depalo Japan: Case for a Taylor Rule? A Simple Approach , 2006 .

[24]  A. C. Rencher Methods of multivariate analysis , 1995 .

[25]  D. Scharfstein,et al.  Herd Behavior and Investment , 1990 .

[26]  Peter Richmond A roof over your head; house price peaks in the UK and Ireland , 2007 .

[27]  Peter Winker,et al.  A global optimization heuristic for estimating agent based models , 2003, Comput. Stat. Data Anal..

[28]  Florian Wagener,et al.  Bifurcation Routes to Volatility Clustering under Evolutionary Learning , 2008 .

[29]  Gilles Teyssière,et al.  Testing for bubbles and change-points , 2005 .

[30]  E. Fama,et al.  The Equity Premium , 2001 .