Volatility co-movements: a time scale decomposition analysis

Abstract

In this paper we are interested in detecting contagion from US to European stock market volatilities in the period immediately after the Lehman Brothers’ collapse. The analysis, based on a factor decomposition of the covariance matrix of implied and realized volatilities, is carried for different sub-samples (identified as normal and crisis periods) and across different (high) frequency bands. In particular, the analysis is split in two stages. In the first stage, we retrieve the time series of wavelet coefficients for each volatility series for high frequency scales, using the Maximal Overlapping Discrete Wavelet transform and, in a second stage, we apply Maximum Likelihood for a factor decomposition of the short-run covariance matrix.Given our focus on the standardized factor loadings associated with the US shock (to control for an heteroscedasticity bias), the empirical findings show no evidence of contagion from the US stock market volatility in realized volatility to all the European countries, while for implied volatility we find a weak evidence of contagion which depends on the scale (the only country not influenced being Netherlands).