Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9905305

Scaling of the distribution of fluctuations of financial market indices

Parameswaran Gopikrishnan·Vasiliki Plerou·Luis A. Nunes Amaral·Martin Meyer·H. Eugene Stanley
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the distribution of fluctuations over a time scale $Δt$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $Δt$, where $Δt$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $Δt \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $α\approx 3$, well outside the stable Lévy regime $0 < α< 2$. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of $α$ consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than $(Δt)_{\times} \approx 4$ days, our results are consistent with slow convergence to Gaussian behavior.

Explore related subjects

cond-mat.stat-mechcond-mat.dis-nnq-fin.ST

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Parameswaran Gopikrishnan, Vasiliki Plerou, Luis A. Nunes Amaral, Martin Meyer, H. Eugene Stanley. 1999-05-20. Scaling of the distribution of fluctuations of financial market indices. https://doi.org/10.1103/physreve.60.5305

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A General Solution for Network Models with Pairwise Edge Coupling

Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous results obtained for specific interaction structures. We use the Hubbard-Stratonovich transform to show that such higher order models can be decoupled into families of effectively separable random graph models, which might be enhanced with auxiliary, possibly multi-valued, parameters identifying the thermodynamical phase of the system. Moreover, given the diagonalizability of couplings between links, we carry out the full computation of the partition functions and discuss why in some cases they can effectively reduce to the one for the Mean-Field case.

cond-mat.stat-mech↗
arXiv2026

Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations

We develop a dynamic theory of eikonal attenuation and mutual coherence for a quantum particle propagating through equilibrium Coulomb fluctuations. The one-particle length $\ell$ is the attenuation length of the ensemble-averaged retarded propagator, not an Anderson localization length or a transport mean free path. For a collisionless classical one-component plasma (OCP), the potential spectrum follows from the fluctuation--dissipation theorem and the RPA dielectric function. In suitable plasma parameter windows, both fast and slow probe regimes are physically meaningful. Fast probes recover the Coulomb logarithm with the dynamical infrared length $v/ω_{\rm p}$. Slow probes yield $G(v)\propto v$ and, in the controlled weak branch, $\ell\propto k$. We derive an exact finite-thickness mutual-coherence expression and a closed slow-regime transverse scaling function. Within the controlled slow-OCP and thick-slab window, the logarithmic two-ray visibility scales as $v^{-1}$ at fixed transverse separation, in contrast to the $v^{-2}$ dependence for frozen finite-slab fluctuations. For a symmetric diffusive electrolyte, linearized stochastic density functional theory gives the exact on-shell result $G_{\rm el}(v)=(m^2C/\hbar^4)\operatorname{arsinh}[v/(2Dκ)]$, where $C=k_{\mathrm B}Tq_0^2/(4π\varepsilon_b)$. For ordinary liquid electrolytes, the slow diffusive limit is inaccessible within the spatial eikonal regime and is therefore a formal asymptote. The physically relevant electrolyte limit is instead that of a fast probe, $v\gg Dκ$, where the diffusive charge relaxation generates an intrinsic infrared length $v/(Dκ^2)$ absent from the quasi-static theory.

cond-mat.stat-mech↗
arXiv2026

Planckian dissipation from classical hydrodynamics

Hydrodynamics describes the long-time, long-distance dynamics of interacting quantum systems by classical equations, yet at low temperature quantum fluctuations might eventually invalidate this classical picture. Here we ask what it takes for a quantum system to sustain a consistently classical hydrodynamic description. Our starting point is the quantum fluctuation-dissipation theorem which, when read in the time domain, acts as a blurring of the fine details of correlation functions on a Planckian time-scale. We analyse how this blurring interacts with the diffusive large-deviation form of correlators assuming the existence of a hydrodynamic light cone velocity, and show that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. We illustrate the mechanism on three phenomenological hydrodynamic equations - diffusion, telegraph and diffusive-telegraph. Preserving a finite classical region as the temperature is lowered forces the current relaxation rate to be bounded from above by the Planckian rate. This bound connects to bounds on diffusivity, equilibration time and shear viscosity. In this way, a Planckian bound on dissipation emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.

cond-mat.stat-mech↗