Related papers: Levy Matrices and Financial Covariances
We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial…
We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical…
Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…
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 L\'evy flights in two dimensions (2D). The efficacy of our proposed model is…
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…
Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…
We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…
A new methodology has been introduced to clean the correlation matrix of single stocks returns based on a constrained principal component analysis using financial data. Portfolios were introduced, namely "Fundamental Maximum Variance…
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
Complex systems are usually non-stationary and their dynamics is often dominated by collective effects. Collectivity, defined as coherent motion of the whole system or of some of its parts, manifests itself in the time-dependent structures…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500 which corresponds to…
We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a L\'evy Stable (fat-tailed) distribution. L\'evy random matrices are known to demonstrate non-ergodic behaviour through the…
We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise…