Booms and bursts of asst markets: empirical results and a model based upon the Fokker-Plank equation

Bubbles and bursts of the Japanese real estate and stock markets in the last two decades were the boom and bust at the maximum scale of the late twentieth century. Why did the burst occur? In this paper we study statistical properties of ensemble of stock prices and land prices in Japan, corresponding to the period of bubbles and crashes. We investigate a database of the assessed value of land covering the 22-years period between 1981-2002. From the data for each of the 22 annual intervals we form the ensembles of the land prices over 10,000 points. We also select 1200 stocks traded in the Tokyo Stock Exchange and form a statistical ensemble of daily stock prices for each of the trading days. We found some common properties of the ensembles of land prices and stock prices. In particular we found that the tail of the cumulative distributions of ensembles of land prices and stock prices is accurately described by a power-law distribution, and furthermore that the power-law exponent decreases in the period of bull markets, and inversely increases in the period of bear markets. We next propose a model based upon the Fokker-Plank equation, which describes the dynamics of the ensemble distribution in order to give an explanation of a mechanism leading bubbles to crashes.