6533b85bfe1ef96bd12bbeef

RESEARCH PRODUCT

Correlation, hierarchies, and networks in financial markets

Fabrizio LilloFabrizio LilloMichele TumminelloRosario N. Mantegna

subject

Organizational Behavior and Human Resource ManagementEconomics and EconometricsPhysics - Physics and SocietyCorrelation based networkKullback–Leibler divergenceStability (learning theory)FOS: Physical sciencesKullback–Leibler distancePhysics and Society (physics.soc-ph)computer.software_genreHierarchical clusteringFOS: Economics and businessCorrelationMultivariate analysis Hierarchical clustering Correlation based networks Bootstrap validation Factor models Kullback–Leibler distancePortfolio Management (q-fin.PM)Bootstrap validationQuantitative Finance - Portfolio ManagementMathematicsFactor analysisStatistical Finance (q-fin.ST)Covariance matrixMultivariate analysiQuantitative Finance - Statistical FinanceHierarchical clusteringFactor modelTree (data structure)Physics - Data Analysis Statistics and ProbabilityData miningPortfolio optimizationcomputerData Analysis Statistics and Probability (physics.data-an)

description

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of the correlation matrix are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback-Leibler distance.

yearjournalcountryeditionlanguage
2010-01-01
10.1016/j.jebo.2010.01.004http://hdl.handle.net/10447/45654