The effect of crude oil prices on US financial and economic variables is well documented in the literature. Hamilton (1996) uses an impulse response approach to show that US recessions were triggered by increases in oil prices. Ghouri (2006), using a linear model, finds that West Texas Intermediate (WTI) oil prices are inversely related to monthly US stock market returns.

Hammoudeh et al. (2004), using a GARCH methodology, find little evidence of spillover effects from oil prices to US stock prices. Elyasiani et al. (2012) compare specific industry sectors in the US stock market and find that, at industry level, there is strong evidence that global oil price volatility constitutes an asset price risk factor for most indices. Mollick and Assefa (2013) investigate the effect of oil on Standard & Poor’s (S&P) 500, Dow Jones, Nasdaq, and Russell 2000 index returns. The authors, also using a GARCH approach, show that US stock returns and WTI oil returns were, to some extent, negatively affected by both the oil prices and the exchange rate prior to the 2007 financial crisis. Moreover, their findings show that, after the onset of the financial crisis, stock returns were positively affected by oil prices and less affected by the exchange rate.

Nazlioglu et al. (2015) use an impulse response function methodology to examine the relationship between WTI and financial stress indices. The analysis, conducted by dividing the sample into a pre-2008 and a post-2008 crisis, shows evidence of significant spillovers in mean as well as in variance. Another recent study, by Salisu and Oloko (2015), considers a VARMA–BEKK–AGARCH (vector autoregressive moving average—Baba–Engle–Kraft–Kroner—asymmetric GARCH) approach to show that stock prices in the United States were more strongly affected by oil prices in the postcrisis period than they had been in the precrisis period.

Huang et al. (1996) use a vector autoregression (VAR) framework to investigate the causality between oil future prices and US stock prices and find weak evidence in terms of return volatility spillover for the period 1979–83. Using a similar approach, Kilian and Park (2009) investigate the relationship between oil and stock prices in the United States by looking at US oil refiners’ acquisition costs to find that US stock prices react differently depending on whether shocks are driven by demand or by supply, while Kang et al. (2014) replace stock prices with bond prices to find that demand and supply shocks originating from oil prices account for strong variations in the US bond market.

Balcilar and Ozdemir (2013) find evidence of nonlinearity between stock prices and oil prices and use a Markov switching model to argue that oil future prices might be a reliable predictor of the S&P 500 index. Alsalman and Herrera (2013), by means of the simultaneous equation method, find that an increase in the price of oil has an effect on UK stock indices up to 1 year ahead. Conrad et al. (2014) consider a modified dynamic conditional correlations–mixed data sampling (DCC–MIDAS) and find a positive oil–stock correlation during recessions and a negative one during economic expansions.

Park and Ratti (2008) and Apergis and Miller (2009) study several developed countries and find that the stock market is affected by positive oil shocks only in Norway (an oil exporter country). Arouri et al. (2011a) use a multifactor asset pricing model for 12 weekly European industrial sector indices and report evidence of substantial returns and volatility spillovers between oil and stock market prices. Arouri et al. (2011b) use a VAR–GARCH(1,1) model to test the relationship between daily oil and stock prices within the Gulf Cooperation Council (GCC) region, and show that oil prices tend to affect positively several stock markets in the region, while the volatility from GCC stock markets to oil markets is nearly absent. Jouini (2013) models weekly stock returns in Saudi Arabia from 2007 until 2011 by means of a VAR–GARCH model; results show evidence of significant and bidirectional spillovers between the Saudi Market Index and oil prices. Jouini and Harrathi (2014) consider a BEKK–GARCH model to revisit the empirical evidence regarding the volatility interactions among GCC stock markets and oil prices for the period 2005–11. Their findings suggest volatility spillover running from stock price volatility into oil market volatilities and vice versa. Zarour (2006) uses a VAR process to show that, while all GCC stock markets are affected by oil price shocks, Saudi and Omani stock market returns also affect oil prices. Lescaroux and Mignon (2008) examine the short- and long-run relationships between WTI oil prices and macroeconomic and financial indicators for oil exporting (including the GCC) and oil importing countries based on causality tests, cross-correlations, and cointegration techniques. Their analysis indicates that there exists a strong Granger causality running from oil to share prices, especially for oil exporting countries. Furthermore, oil prices were found to lead (countercyclically) share prices for the majority of the investigated countries.

Using a BEKK–GARCH model, Malik and Hammoudeh (2007) find that there is a significant volatility spillover running from oil to stock markets in the United States and GCC countries. Filis et al. (2011) compared three oil importing countries (Germany, the Netherlands, and the United States) and three oil exporting countries (Brazil, Canada, and Mexico) using a DCC–GARCH framework. Their results suggest that the relationship between oil and stock prices depends on the nature of the shocks; that is, demand shocks caused by drastic events, such as war, might affect stock markets more significantly than supply-side shocks originated by production cuts. The authors also find a correlation between lagged oil prices and stock market returns. Finally, Wang et al. (2013) use a structural VAR (SVAR) model to examine both oil importing countries (China, France, Germany, India, Italy, Japan, South Korea, the United Kingdom, and the United States) and oil exporting countries (Canada, Saudi Arabia, Kuwait, Mexico, Norway, Russia, and Venezuela). Their findings indicate that oil supply uncertainty can depress the stock markets of both oil exporter and importer countries.

The remainder of the chapter is structured as follows. Section 2 discusses the econometric method, whereas Section 3 presents the data and discusses the empirical results. Section 4 concludes.

where x_t = (stock_t, oil_t). The parameter vectors of the mean Eq. 3.1 are the constant α = (α₁,α₂) and the autoregressive term β = (β₁₁, 0 | 0,β₂₂). The residual vector u_t = (e_1,t,e_2,t) is bivariate and normally distributed, u_t | I_t − 1 ∼ (0, H_t), with a corresponding, conditional variance–covariance matrix given by

where

Eq. 3.3 models the dynamic process of H_t as a linear function of its own past values H_t − 1 and the past values of the squared innovations $(e_{1,t-1}^2{e}_{2,t-1}^2)$. The BEKK model guarantees, by construction, that the covariance matrix in the system is positive definite. Given a sample of T observations, a vector of unknown parameters θ, and a 2 × 1 vector of variables x_t, the conditional density function for the model, Eq. 3.1, is:

The log-likelihood function is:

Standard errors are calculated using the quasi-maximum likelihood method of Bollerslev and Wooldridge (1992), which is robust to the distribution of the underlying residuals.