A Pratical Approach to Financial Crisis Indicators Based on Random Matrices

Antoine Kornprobst () and Raphael Douady ()
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Antoine Kornprobst: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: The aim of this work is to build financial crisis indicators based on market data time series. After choosing an optimal size for a rolling window, the market data is seen every trading day as a random matrix from which a covariance and correlation matrix is obtained. Our indicators deal with the spectral properties of these covariance and correlation matrices. Our basic financial intuition is that correlation and volatility are like the heartbeat of the financial market: when correlations between asset prices increase or develop abnormal patterns, when volatility starts to increase, then a crisis event might be around the corner. Our indicators will be mainly of two types. The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix. As reference distribution we will use the theoretical Marchenko Pastur distribution and, mainly, simulated ones using a random matrix of the same size as the empirical rolling matrix and constituted of Gaussian or Student-t coefficients with some simulated correlations. The idea behind this first type of indicators is that when the empirical distribution of the spectrum of the covariance matrix is deviating from the reference in the sense of Hellinger, then a crisis may be forthcoming. The second type of indicators is based on the study of the spectral radius and the trace of the covariance and correlation matrices as a mean to directly study the volatility and correlations inside the market. The idea behind the second type of indicators is the fact that large eigenvalues are a sign of dynamic instability.

Keywords: quantitative finance; Econometrics; Mathematical methods; Statistical simulation methods; forecasting and prediction methods; large data sets modeling and analysis; Computational techniques; simulation modeling; financial crises; random matrix theory; Finance quantitative; méthodes mathématiques; Econométrie; méthodes de simulation statistique; méthodes de prévision; analyse de grandes bases de données; méthodes de calcul; simulations; crises financière; matrices aléatoires (search for similar items in EconPapers)
Date: 2015-05
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01169307v1
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Published in 2015

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Related works:
Working Paper: A Pratical Approach to Financial Crisis Indicators Based on Random Matrices (2015)
Working Paper: A Practical Approach to Financial Crisis Indicators Based on Random Matrices (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-01169307

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