Dissecting financial markets: Sectors and states

By analyzing a large data set of daily returns with data clustering technique, we identify economic sectors as clusters of assets with a similar economic dynamics. The sector size distribution follows Zipf's law. Secondly, we find that patterns of daily market-wide economic activity cluster into classes that can be identified with market states. The distribution of frequencies of market states shows scale-free properties and the memory of the market state process extends to long times ($\sim 50$ days). Assets in the same sector behave similarly across states. We characterize market efficiency by analyzing market's predictability and find that indeed the market is close to being efficient. We find evidence of the existence of a dynamic pattern after market's crashes.Comment: 6 pages 4 figures. Additional information available at http://www.sissa.it/dataclustering/fin

Critical exponents of the anisotropic Bak-Sneppen model

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.Comment: 8 pages, three figures included with psfig, some rewriting, + extra figure and table of exponent

Financial instability from local market measures

We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random markets using techniques borrowed from statistical mechanics of disordered systems. We show that, depending on the number of financial instruments available and on the heterogeneity of local measures, the market moves from an arbitrage-free phase to an unstable one, where the complexity of the market - as measured by the diversity of financial instruments - increases, and arbitrage opportunities arise. A sharp transition separates the two phases. Focusing on two different classes of local measures inspired by real markets strategies, we are able to analytically compute the critical lines, corroborating our findings with numerical simulations.Comment: 17 pages, 4 figure

High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent $\alpha$ decays not faster than $\alpha\sim 1/d$ for large $d$. This implies the absence of a finite upper critical dimension.Comment: RevTeX, 4 pages, 2 figures. To appear in Phys. Rev.

A Prototype Model of Stock Exchange

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate his assets by speculating on the price's fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets.Comment: LaTex, 4 pages, 4 Encapsulated Postscript figures, uses psfi

Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude

Single photonics at telecom wavelengths using nanowire superconducting detectors

Single photonic applications - such as quantum key distribution - rely on the transmission of single photons, and require the ultimate sensitivity that an optical detector can achieve. Single-photon detectors must convert the energy of an optical pulse containing a single photon into a measurable electrical signal. We report on fiber-coupled superconducting single-photon detectors (SSPDs) with specifications that exceed those of avalanche photodiodes (APDs), operating at telecommunication wavelength, in sensitivity, temporal resolution and repetition frequency. The improved performance is demonstrated by measuring the intensity correlation function g(2)(t) of single-photon states at 1300nm produced by single semiconductor quantum dots (QDs).Comment: 7 pages, 5 figures - submitted 12 OCT 200

Generalized minority games with adaptive trend-followers and contrarians

We introduce a simple extension of the minority game in which the market rewards contrarian (resp. trend-following) strategies when it is far from (resp. close to) efficiency. The model displays a smooth crossover from a regime where contrarians dominate to one where trend-followers dominate. In the intermediate phase, the stationary state is characterized by non-Gaussian features as well as by the formation of sustained trends and bubbles.Comment: 4 pages, 6 figure