We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade...

We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a...

The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and $JPY/DEM$ and $DEM/USD$ currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and...

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we...

Here we analyze tick data of yen–dollar exchange using random walk methods. We find that there exists a characteristic time scale approximately at 10 min. According to the results at time scales shorter than 10 min, the market exhibits anti-persistence meaning that it self-organizes so as to...

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining...

The existence of a phase transition in a computer network model is indicated by an abrupt change in packet density, critical slowing down and fractal properties of the characteristic time series. The network operates most efficiently in the vicinity of the critical point.

In order to describe price changes in open markets we introduce a virtual balanced price which is determined by the distribution of dealers’ expectation at a time. The dealers do not know directly the virtual balanced price but they can only guess it from the time series of market prices. By...

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of...