Inverse cubic law for the distribution of stock price variations

Abstract:The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period January 1994 - December 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent $$a \approx 3$$ , well outside the Lévy regime $$(0 < \alpha < 2)$$ .

• Publication year

  1998

• Venue

  The European Physical Journal B - Condensed Matter and Complex Systems

• Publication date

  1998-03-30

• Fields of study

  Mathematics, Physics, Economics

• Identifiers
  DOI 10.1007/s100510050292arXiv cond-mat/9803374
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Business

  1998cited by this paper
• Théorie des risques financiers

  1997cited by this paper
• Théorie de l'addition des variables aléatoires

  1955cited by this paper

• The Impact of Trump-Era Tariffs on Financial Market Efficiency

  2026cites this paper
• Understanding emerging properties through multi-scaling nature in the financial market

  2026cites this paper
• Extensions to the Wealth Tax Neutrality Framework

  2026cites this paper
• Novel Market Temperature Definition Through Fluctuation Theorem: A Statistical Physics Framework for Financial Crisis Prediction

  2025cites this paper
• Characterizing asymmetric and bimodal long-term financial return distributions through quantum walks

  2025cites this paper
• Scaling and shape of financial returns distributions modeled as conditionally independent random variables

  2025cites this paper
• Economic Feasibility and Decarbonization Incentives of Sugarcane Biogas Production Pathways

  2025cites this paper
• Filtering amplitude dependence of correlation dynamics in complex systems: application to the cryptocurrency market

  2025cites this paper
• Modeling and Generating Extreme Fluctuations in Time Series with a Multilayer Linear Response Model

  2025cites this paper
• Boltzmann Price: Toward Understanding the Fair Price in High-Frequency Markets

  2025cites this paper
• Stock market simulator using hidden Markov generative model and its application in risk measurement

  2025cites this paper
• Detrended Cross-Correlations and Their Random Matrix Limit: An Example from the Cryptocurrency Market

  2025cites this paper
• Radially geometric stable distributions and processes

  2025cites this paper
• Growth of Science: How long will the United States uphold its position?

  2024cites this paper
• Market Ecology: Trading Strategies and Market Volatility

  2024influential citation
• Singular Stochastic Differential Equations for Time Evolution of Stocks Within Non-white Noise Approach

  2024cites this paper
• Pricing efficiency in cryptocurrencies: The case of centralized and decentralized markets

  2024cites this paper
• On the potential of quantum walks for modeling financial return distributions

  2024cites this paper
• Multivariate distributions in non-stationary complex systems II: Empirical results for correlated stock markets

  2024cites this paper
• Evolutionary dynamics in financial markets with heterogeneities in investment strategies and reference points

  2023cites this paper
• Tempered geometric stable distributions and processes

  2023cites this paper
• Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

  2023cites this paper
• Modeling and simulation of financial returns under non-Gaussian distributions

  2023cites this paper
• Kajian Teoritik Persamaan Diferensial Stokastik bagi Kurs Mata Uang (Forex), Kajian Khusus : Kurs IDR/USD

  2023cites this paper
• Correlation versus co-fractality: Evidence from foreign-exchange-rate variances

  2023cites this paper
• Perishable Goods versus Re-tradable Assets: A Theoretical Reappraisal of a Fundamental Dichotomy

  2023cites this paper
• Revisiting Stylized Facts for Modern Stock Markets

  2023cites this paper
• Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation

  2023cites this paper
• Properties of VaR and CVaR Risk Measures in High-Frequency Domain: Long–Short Asymmetry and Significance of the Power-Law Tail

  2023cites this paper
• Age and market capitalization drive large price variations of cryptocurrencies

  2023cites this paper
• COVID-19 and REITs Crash: Predictability and Market Conditions

  2023influential citation
• Revisiting Cont's stylized facts for modern stock markets

  2023cites this paper
• Price fairness: Clean energy stocks and the overall market

  2023cites this paper
• Universal to nonuniversal transition of the statistics of rare events during the spread of random walks.

  2023cites this paper
• Dynamics of Hierarchical Clustering in Stocks Market During Financial Crises

  2022cites this paper
• Technological Change and Market Conditions: Evidence from Bitcoin Fork

  2022cites this paper
• Genuine multifractality in time series is due to temporal correlations.

  2022cites this paper
• Preference heterogeneity in Bitcoin and its forks' network

  2022cites this paper
• Bank Capital Regulation for Market Risk”

  2022cites this paper
• Ja n 20 01 Multi-dimensional Rational Bubbles and fat tails ∗

  2022cites this paper
• A simple learning agent interacting with an agent-based market model

  2022cites this paper
• Precision Measurement of the Return Distribution Property of the Chinese Stock Market Index

  2022cites this paper
• Perishable Goods versus Re-tradable Assets: A Theoretical Perishable Goods versus Re-tradable Assets: A Theoretical Reappraisal of a Fundamental Dichotomy Reappraisal of a Fundamental Dichotomy

  2022cites this paper
• Mechanism of Investor Behavior Propagation in Stock Market

  2022cites this paper
• Extremity in bitcoin market activity

  2022cites this paper
• The predictive power of power-laws: An empirical time-arrow based investigation

  2022cites this paper
• Interplay between nonlinear Fokker–Planck equation and stochastic differential equation

  2022cites this paper
• Analysis of PER, DER, and ROA on the Textile Companies’ Performance Listed on Indonesian Stock Exchange

  2021cites this paper
• Econophysics of cryptocurrency crashes: a systematic review

  2021cites this paper
• Re-tradable Assets, Speculation, and Economic Instability Re-tradable Assets, Speculation, and Economic Instability

  2021cites this paper
• Modeling the cryptocurrency return distribution via Laplace scale mixtures

  2021cites this paper
• Predictors of oil shocks. Econophysical approach in environmental science

  2021cites this paper
• A computational proposal for a robust estimation of the Pareto tail index: An application to emerging markets

  2021cites this paper
• Random Walks

  2021cites this paper
• Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

  2021cites this paper
• Space-time fractional porous media equation: Application on modeling of S&P500 price return.

  2021cites this paper
• Financial Return Distributions: Past, Present, and COVID-19

  2021cites this paper
• The Stock Market Model with Delayed Information Impact from a Socioeconomic View

  2021cites this paper
• Time-varying properties of asymmetric volatility and multifractality in Bitcoin

  2021cites this paper
• Econophysics of cryptocurrency crashes: an overview

  2021cites this paper
• Complexity and Persistence of Price Time Series of the European Electricity Spot Market

  2021cites this paper
• News-Driven Expectations and Volatility Clustering

  2020cites this paper
• Local and Non-local Fractional Porous Media Equations.

  2020cites this paper
• Stochastic analysis using public data for forecasting of epidemic spreading of the novel coronavirus disease

  2020cites this paper
• Bypassing the truncation problem of truncated Lévy flights

  2020cites this paper
• CARF Working Paper

  2020cites this paper
• Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks

  2020cites this paper
• FRTB and Fat Tails

  2020cites this paper
• Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

  2020cites this paper
• Heavy tailed distributions in closing auctions

  2020influential citation
• Combination of transition probability distribution and stable Lorentz distribution in stock markets

  2020cites this paper
• Recent scaling properties of Bitcoin price returns

  2020cites this paper
• Association between COVID-19 cases and international equity indices

  2020cites this paper
• Trade clustering and power laws in financial markets

  2020cites this paper
• Econophysical bourse volatility – Global Evidence

  2020cites this paper
• Fat Tails Arise Endogenously in Asset Prices From Supply/Demand, With or Without Jump Processes

  2020cites this paper
• Trade clustering and power laws in financial markets

  2020cites this paper
• Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

  2020cites this paper
• Information Flow Networks of Chinese Stock Market Sectors

  2020cites this paper
• A note on power-law cross-correlated processes

  2020cites this paper
• Two-dimensional stochastic dynamics as model for time evolution of the financial market

  2020cites this paper
• Analyses on Volatility Clustering in Financial Time-Series Using Clustering Indices, Asymmetry, and Visibility Graph

  2020cites this paper
• Correlation noise and delay time enhanced stability of electricity futures market

  2019cites this paper
• Dynamic behaviors and measurements of financial market crash rate

  2019cites this paper
• Market efficiency is truly enhanced in sub-second trading market

  2019cites this paper
• Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis

  2019cites this paper
• Endogenous liquidity crises

  2019cites this paper
• Nonlinear Stochastic Equation within an Itô Prescription for Modelling of Financial Market

  2019cites this paper
• Coherence resonance-like and efficiency of financial market

  2019cites this paper
• Breaks down of the modeling of the financial market with addition of non-linear terms in the Itô stochastic process

  2019cites this paper
• Development of an agent-based speculation game for higher reproducibility of financial stylized facts

  2019cites this paper
• Regularities in stock markets

  2019cites this paper
• Signatures of the Crypto-Currency Market Decoupling from the Forex

  2019cites this paper
• Anomaly detection in Bitcoin market via price return analysis

  2019cites this paper
• VC correlation analysis on the overnight and daytime return in Japanese stock market

  2019cites this paper
• Agglomerative likelihood clustering

  2019cites this paper
• Multiscale cross-correlations and triangular arbitrage opportunities in the Forex

  2019cites this paper
• High frequency trading strategies, market fragility and price spikes: an agent based model perspective

  2018cites this paper
• Stochastic process with multiplicative structure for the dynamic behavior of the financial market

  2018cites this paper
• Tail probabilities for short-term returns on stocks

  2018influential citation