A Wavelet-heterogeneous Index of Market Shocks for assessing the Magnitude of Financial Crises

Abstract. An accurate quantitative definition of financial crisis requires a universal and robust scale for measuring market shocks. Following Zumbach et al. (2000) and Maillet et Michel (2003), we propose a new quantitative measure of financial disturbances, which captures the heterogeneity of investor horizons – from day traders to pension funds. The indicator resides on a multi-resolution analysis of market volatility, each scale corresponding to various investment horizons and different data frequencies. This new risk measure, called “Wavelet-heterogeneous Index of Market Shocks ” (WhIMS), is based on the combination of two methods: the Wavelet Packets Sub-band Decomposition and the constrained Independent Component Analysis (See Kopriva and Serˇsić, 2007 and Lu and Rajapakse, 2005). We apply this measure on the French stock markets (high frequency CAC40) to date and gauge the severity of financial crises.