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Version: 2009-10-07 Motivated by recent developments in light of the sub-prime and subsequent financial crisis we fit two different vector autoregressive generalized conditional heteroscedastic (VAR-GARCH) models to three financial indices with the aim of understanding the development of dependency structures between credit spreads and other macroeconomic variables. Our analysis includes daily quotes from June 2004 to April 2009 of the iTraxx Europe index, the Dow Jones Euro Stoxx 50 index, and the Dow Jones VStoxx index. We propose a robust, time-varying modeling approach concerning the conditional mean, and a BEKK versus DCC-GARCH approach concerning the conditional covariance. Furthermore we allow for a parsimonious model specification by setting insignificant coefficients to zero. Our empirical results indicate that the autoregressive coefficients vary strongly with time and even change their signs. Well-known interrelations, such as the negative correlation between CDS ’ and stocks are lost through the financial crisis. The conditional covariance estimates in the BEKK and DCC model are fairly similar, given the difference in the number of model parameters. We found evidence of strongly varying conditional variances and correlations, with dependencies increasing after the outbreak of the financial crisis. This knowledge may help to improve decision tools in the financial industry, especially in areas such as asset pricing, portfolio selection, and risk management.

Abstract: This paper examines the inclusion of the dollar/euro exchange rate together with four important and highly traded commodities- aluminum, copper, gold and oil- in symmetric and asymmetric multivariate GARCH and DCC models. The inclusion of exchange rate increases the significant direct and indirect past shock and volatility effects on future volatility between the commodities in all the models. Model 2, which includes the business cycle industrial metal copper and not aluminum, displays more direct and indirect transmissions than does Model 3, which replaces the business cycle-sensitive copper with the highly energy-intensive aluminum. The asymmetric effects are the greatest in Model 3 because of the high interactions between oil and aluminum. Optimal portfolios should have more euro currency than commodities, and more copper and gold

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Abstract: Crude oil price volatility has been analyzed extensively for organized spot, forward and futures markets for well over a decade, and is crucial for forecasting volatility and Value-at-Risk (VaR). There are four major benchmarks in the international oil market, namely West Texas Intermediate (USA), Brent (North Sea), Dubai/Oman (Middle East), and Tapis (Asia-Pacific), which are likely to be highly correlated. This paper analyses the volatility spillover and asymmetric effects across and within the four markets, using three multivariate GARCH models, namely the constant conditional correlation (CCC), vector ARMA-GARCH (VARMA-GARCH) and vector ARMA-asymmetric GARCH (VARMA-AGARCH) models. A rolling window approach is used to forecast the 1-day ahead conditional correlations. The paper presents evidence of volatility spillovers and asymmetric effects on the conditional variances for most pairs of series. In addition, the forecast conditional correlations between pairs of crude oil returns have both positive and negative trends. Moreover, the optimal hedge ratios and optimal portfolio weights of crude oil across different assets and market portfolios are evaluated in order to provide important policy implications for risk management in crude oil markets.

their helpful comments and suggestions. In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. Some recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC, Exponentially Weighted Moving Average, and covariance shrinking, using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem. Keywords: Covariance forecasting, model confidence set, model ranking, MGARCH, model comparison.

Abstract: This paper investigates the conditional correlations and volatility spillovers between crude oil returns and stock index returns. Daily returns from 2 January 1998 to 4 November 2009 of the crude oil spot, forward and futures prices from the WTI and Brent markets, and the FTSE100, NYSE, Dow Jones and S&P500 index returns, are analysed using the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer, Hoti and Chan (2008), and DCC model of Engle (2002). Based on the CCC model, the estimates of conditional correlations for returns across markets are very low, and some are not statistically significant, which means the conditional shocks are correlated only in the same market and not across markets. However, the DCC estimates of the conditional correlations are always significant. This result makes it clear that the assumption of constant conditional correlations is not supported empirically. Surprisingly, the empirical results from the VARMA-GARCH and VARMA-AGARCH models provide little evidence of volatility spillovers between the crude oil and financial markets. The evidence of asymmetric effects of negative and positive shocks of equal magnitude on the conditional variances suggests that VARMA-AGARCH is superior to VARMA-GARCH and