Volatility Spillover and Multivariate Volatility Impulse Response Analysis of GFC News Events

This paper applies two measures to assess spillovers across markets: the Diebold Yilmaz (2012) Spillover Index and the Hafner and Herwartz (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility estimates taken from the Oxford Man RV library, running from the beginning of 2000 to October 2016, for the S&P500 and the FTSE, plus ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index, from 3 January 2005 to 31 January 2015. Both data sets capture both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The key difference between the measures is that the spillover index captures an average of spillovers over a period, whilst volatility impulse responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. The VIRF provide information about the impact of independent shocks on volatility. In the latter analysis, we explore the impact of three different shocks, the onset of the GFC, which we date as 9 August 2007 (GFC1). It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, (GFC2). The third shock is 9 May 2010. Our modelling includes leverage and asymmetric effects undertaken in the context of a multivariate GARCH model, which are then analysed using both BEKK and diagonal BEKK (DBEKK) models. A key result is that the impact of negative shocks is larger, in terms of the effects on variances and covariances, but shorter in duration, in this case a difference between three and six months.

Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers

The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988, 39(1-2), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESV-ALM, and the finite sample properties of the quasi-maximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. The volatility and co-volatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and co-volatility.