Simulations of agent-based models have shown that the stylized facts (unit-root, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of non-linearity and interactions, often...

The problems related to the application of multivariate GARCH models to a market with a large number of stocks are solved by restricting the form of the conditional covariance matrix. It contains one component describing the market and a second simple component to account for the remaining...

The problems related to the application of multivariate GARCH models to a market with a large number of stocks are solved by restricting the form of the conditional covariance matrix. It contains one component describing the market and a second simple component to account for the remaining...

We perform a careful spectral analysis of the correlation structures observed in real and financial returns for a large pool of long-lived US corporations, and find that financial returns are characterized by strong collective fluctuations that are absent from real returns. Once the excessive...

Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust...

Multifractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in...