Imitative and contrarian behaviours are the two typical opposite attitudes of investors in stock markets. We introduce a simple model to investigate their interplay in a stock market where agents can take only two states, bullish or bearish. Each bullish (bearish) agent polls m 'friends' and...

We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. Inspired by an analogy between price dynamics and hydrodynamic turbulence, it models the time scale dependence of the probability distribution...

Using one of the key properties of copulas that they remain invariant under an arbitrary monotonic change of variable, we investigate the null hypothesis that the dependence between financial assets can be modelled by the Gaussian copula. We find that most pairs of currencies and pairs of major...

Are large-scale research programmes that include many projects more productive than smaller ones with fewer projects? This problem of economies of scale is relevant for understanding recent mergers, in particular in the pharmaceutical industry. We present a quantitative theory based on the...

The present article constitutes part II of a series of two reports in which we study the decomposition of synthetic and real financial time-series into a superposition of weighted Hamiltonian cycles on graphs. Part II further analyses the cycle-decomposition method introduced in part I for the...

The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available...

We present a theory of bridge homogeneous volatility estimators for log-price stochastic processes. Starting with the standard definition of a Brownian bridge as the conditional Wiener process with two endpoints fixed, we introduce the concept of an incomplete bridge by breaking the symmetry...

We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's criticism ([A article="1469-7688/1/3/306"] Feigenbaum J A 2001 Quantitative Finance1 346-60 [/A]) and show how it can be refuted. Feigenbaum's main...

Lux and Sornette have demonstrated that the tails of the unconditional distributions of price differences and of returns associated with the model of rational bubbles of Blanchard and Watson follow power laws (i.e. exhibit hyperbolic decline), with an asymptotic tail exponent μ1 over an...

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. We develop a battery of new non-parametric and parametric tests to characterize the distributions of empirical returns of...