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.

Research highlights► A behavior model describing the appearance and burst of financial bubbles. ► Discrete time formulas and corresponding continuous time formulas for the model. ► The clear mechanism of each kind of financial bubbles. ► Empirical studies using annual observations of the S&P 500 index.