A 2D Levy-flight model for the complex dynamics of real-life financial markets
arXiv:2202.12067 · doi:10.1063/5.0082926
Abstract
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a geometric law between the gyration radius and the total length of the path, i.e., . We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time -- a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of a 2D Lévy flights with index from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.
arXiv comment5 figures, 9 pages
References in corpus (41)
- Hierarchical Structure in Financial Markets
- Level-Spacing Distributions and the Airy Kernel
- Noise Dressing of Financial Correlation Matrices
- Universal and non-universal properties of cross-correlations in financial time series
- A Random Matrix Approach to Cross-Correlations in Financial Data
- Scaling of the distribution of fluctuations of financial market indices
- On Orthogonal and Symplectic Matrix Ensembles
- Dynamics of market correlations: Taxonomy and portfolio analysis
- Communicability in complex networks
- The statistical properties of the volatility of price fluctuations
- Scaling of the distribution of price fluctuations of individual companies
- Localization and Spreading of Diseases in Complex Networks
- The leverage effect in financial markets: retarded volatility and market panic
- Correlations in Economic Time Series
- Dynamic asset trees and Black Monday
- Universal features in the growth dynamics of complex organizations
- Transmission of Information and Herd Behavior: an Application to Financial Markets
- Spectra of complex networks
- Power Law Scaling for a System of Interacting Units with Complex Internal Structure
- Spectra and eigenvectors of scale-free networks
- Quantifying Stock Price Response to Demand Fluctuations
- Large Deviations of Extreme Eigenvalues of Random Matrices
- Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
- Extreme value statistics of correlated random variables: a pedagogical review
- Asset trees and asset graphs in financial markets
- Random Matrix Theory Analysis of Cross Correlations in Financial Markets
- Volatility clustering and scaling for financial time series due to attractor bubbling
- Time dependent cross correlations between different stock returns: A directed network of influence
- Ivory Tower Universities and Competitive Business Firms
- Top eigenvalue of a random matrix: large deviations and third order phase transition
- Correlation, Network and Multifractal Analysis of Global Financial Indices
- Cross-correlation in financial dynamics
- Identifying long-term precursors of financial market crashes using correlation patterns
- Renormalizing Rectangles and Other Topics in Random Matrix Theory
- Optimization of the post-crisis recovery plans in scale-free networks
- Universal Correlations and Power-Law Tails in Financial Covariance Matrices
- Metastable Features of Economic Networks and Responses to Exogenous Shocks
- Financial Market Dynamics: Superdiffusive or not?
- Hysteresis of economic networks in an XY model
- Asymmetric Tsallis distributions for modelling financial market dynamics
- A geometrical imaging of the real gap between economies of China and the United States