The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications to market data we indicate the shortcomings of such...

We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric...

Recently, Ghashghaie et al. have shown that some statistical aspects of fully developed turbulence and exchange rate fluctuations exhibit striking similarities (Nature 381, 767 (1996)). The authors then suggested that the two problems might be deeply connected, and speculated on the existence of...

This paper contains a phenomenological description of the whole U.S. forward rate curve (FRC), based on an data in the period 1990-1996. We find that the average FRC (measured from the spot rate) grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate...

We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback effects of price...

We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to distributions observed in recent empirical studies of high...

We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this...

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the...

We show how one can actually take advantage of the strongly non-Gaussian nature of the fluctuations of financial assets to simplify the calculation of the Value-at-Risk of complex non linear portfolios. The resulting equations are not hard to solve numerically, and should allow fast VaR and...