On Dynamics in An Asset Pricing Model with Heterogeneous Expectations

In this paper we present an interacting-agent model of speculative activity explaining bubbles and crashes in stock markets. We describe stock markets through an infinite-range using model to formulate the tendency of traders getting influenced by the investment attitude of other traders. Bubbles and crashes are understood and described qualitatively and quantitatively in terms of the classical phase transitions. When the interactions among traders become stronger and reach some critical values, a second-order phase transition and critical behaviour can be observed, and a bull market phase and a bear market phase appear. When the system stays at the bull market phase, speculative bubbles occur in the stock market. For a certain range of the external field that we shall call the investment environment, multistability and hysteresis phenomena are observed. When the investment environment reaches some critical values, the rapid changes in the distribution of investment attitude are caused. The first-order phase transition from a bull market phase to a bear market phase is considered as a stock market crash. Furthermore we estimate the parameters of the model using the actual financial data. As an example of large crashes we analyse Japan crisis (the bubble and the subsequent crash in the Japanese stock market in 1987-1992), and show that the good quality of the fits, as well as the consistency of the values of the parameters are obtained from Japan crisis. The results of the empirical study demonstrate that Japan crisis can be explained quite naturally by the model that bubbles and crashes have their origin in the collective crowd behaviour of many interacting agents.Speculative Bubbles; Stock market crash; Phase transition; Mean field approximation; Japan crisis