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A Pratical Approach to Financial Crisis Indicators Based on Random Matrices

Author

Listed:
  • Antoine Kornprobst

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Antoine Kornprobst & Raphaël Douady, 2015. "A Pratical Approach to Financial Crisis Indicators Based on Random Matrices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169307, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01169307
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01169307
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    References listed on IDEAS

    as
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    More about this item

    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;
    All these keywords.

    JEL classification:

    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G01 - Financial Economics - - General - - - Financial Crises

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