| 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
distributions 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. |