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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.

This paper applies the Hafner and Herwartz (2006) (hereafter HH) approach to the analysis of multivariate GARCH models using volatility impulse response analysis. The data set features ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index from the London Stock Exchange, from 3 January 2005 to 31 January 2015. This period captures both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The attraction of the HH approach is that it involves a novel application of the concept of impulse response functions, tracing the effects of independent shocks on volatility through time, while avoiding typical orthogonalization and ordering problems. Volatility impulse response functions (VIRF) provide information about the impact of independent shocks on volatility. HH’s VIRF extends a framework provided by Koop et al. (1996) for the analysis of impulse responses. This approach is novel because it explores the effects of shocks to the conditional variance, as opposed to the conditional mean. HH use the fact that GARCH models can be viewed as being linear in the squares, and that multivariate GARCH models are known to have a VARMA representation with non-Gaussian errors. They use this particular structure to calculate conditional expectations of volatility analytically in their VIRF analysis. A Jordan decomposition of Σ t is used to obtain independent and identically distributed innovations. A general issue in the approach is the choice of baseline volatilities. VIRF is defined as the expectation of volatility conditional on an initial shock and on history, minus the baseline expectation that conditions on history. This makes the process endogenous, but the choice of the baseline shock within the data set makes a difference. We explore the impact of three different shocks, the first marking the onset of the GFC, which we date as 9 August 2007 (GFC1). This began with the seizure in the banking system precipitated by BNP Paribas announcing that it was ceasing activity in three hedge funds that specialised in US mortgage debt. It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, when the US government allowed the investment bank Lehman Brothers to go bankrupt (GFC2). The third shock is 9 May 2010, which marked the point at which the focus of concern switched from the private sector to the public sector. A further contribution of this paper is the inclusion of leverage, or asymmetric effects. Our modelling is undertaken in the context of a multivariate GARCH model featuring pre-whitened return series, which are then analysed using both BEKK and diagonal BEKK models with the t -distribution. 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, in the context of the return series.

This paper applies the Hafner and Herwartz (2006) (hereafter HH) approach to the analysis of multivariate GARCH models using volatility impulse response analysis. The data set features ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index from the London Stock Exchange, from 3 January 2005 to 31 January 2015. This period captures both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The attraction of the HH approach is that it involves a novel application of the concept of impulse response functions, tracing the effects of independent shocks on volatility through time, while avoiding typical orthogonalization and ordering problems. Volatility impulse response functions (VIRF) provide information about the impact of independent shocks on volatility. HH’s VIRF extends a framework provided by Koop et al. (1996) for the analysis of impulse responses. This approach is novel because it explores the effects of shocks to the conditional variance, as opposed to the conditional mean. HH use the fact that GARCH models can be viewed as being linear in the squares, and that multivariate GARCH models are known to have a VARMA representation with non-Gaussian errors. They use this particular structure to calculate conditional expectations of volatility analytically in their VIRF analysis. A Jordan decomposition of Σt is used to obtain independent and identically distributed innovations. A general issue in the approach is the choice of baseline volatilities. VIRF is defined as the expectation of volatility conditional on an initial shock and on history, minus the baseline expectation that conditions on history. This makes the process endogenous, but the choice of the baseline shock within the data set makes a difference. We explore the impact of three different shocks, the first marking the onset of the GFC, which we date as 9 August 2007 (GFC1). This began with the seizure in the banking system precipitated by BNP Paribas announcing that it was ceasing activity in three hedge funds that specialised in US mortgage debt. It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, when the US government allowed the investment bank Lehman Brothers to go bankrupt (GFC2). The third shock is 9 May 2010, which marked the point at which the focus of concern switched from the private sector to the public sector. A further contribution of this paper is the inclusion of leverage, or asymmetric effects. Our modelling is undertaken in the context of a multivariate GARCH model featuring pre-whitened return series, which are then analysed using both BEKK and diagonal BEKK models with the t-distribution. 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, in the context of the return series.

This paper features an application of the Hafner and Herwartz (2006) approach to the analysisof multivariate GARCH models using volatility impulse response analysis. The data set used features tenyears of daily return series for the New York Stock Exchange Index and the FTSE 100 index from theLondon stock Exchange, taken from 3rd January 2005 to January 31st 2015. This period captures both theGlobal Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The attraction ofthe Hafner and Kerwartz (2006) approach is that it involves a novel application of the concept of impulseresponse functions, tracing the effects of independent shocks on volatility through time, whilst avoidingtypical orthogonalization and ordering problems. Volatility impulse response functions (VIRF) provideinformation about the impact of independent shocks on volatility Refereed/Peer-reviewed