The main objective of this paper is to investigate the validity of the much-used assumptions that stock market returns follow a random walk and are normally distributed. For this purpose the concepts of chaos theory and fractals are applied. Two independent models are used to examine price...

In this paper, we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to Malaysian currency, Ringgit Malaysia. These time series are examined piecewise before and after the currency control imposed in 1st September 1998 using the monofractal model based on...

By scientific standards, the accuracy of short-term economic forecasts has been poor, and shows no sign of improving over time. We form a delay matrix of time-series data on the overall rate of growth of the economy, with lags spanning the period over which any regularity of behaviour is...

Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial...

In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of...

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency...

Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an...

As an aggregate measure of the variations in individuals, the analysis of mobility provides a substantial and comprehensive perspective into the complexity of socio-economic systems. In this paper, we introduced the ranking mobility index to measure the ranking variations of the stocks in...

Neural network algorithms are applied to the problem of option pricing and adopted to simulate the nonlinear behavior of such financial derivatives. Two different kinds of neural networks, i.e. multi-layer perceptrons and radial basis functions, are used and their performances compared in...

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We...