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An Empirical Approach to Financial Crisis Indicators Based on Random Matrices

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  • Antoine Kornprobst
  • Raphael Douady

Abstract

The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtained. The financial crisis indicators that we have built deal with the spectral properties of these covariance and correlation matrices and they are of two kinds. 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 representing either a calm or agitated market. 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. The predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective-put strategy.

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  • Antoine Kornprobst & Raphael Douady, 2015. "An Empirical Approach to Financial Crisis Indicators Based on Random Matrices," Papers 1506.00806, arXiv.org, revised Sep 2017.
  • Handle: RePEc:arx:papers:1506.00806
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    Cited by:

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    2. Raphaël Douady, 2019. "Managing the Downside of Active and Passive Strategies: Convexity and Fragilities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02488589, HAL.
    3. Lin, Li & Guo, Xin-Yu, 2019. "Identifying fragility for the stock market: Perspective from the portfolio overlaps network," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 132-151.
    4. Allaj, Erindi & Sanfelici, Simona, 2023. "Early Warning Systems for identifying financial instability," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1777-1803.

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