The purpose of this paper is to investigate volatility spillovers between crude oil futures returns and oil company stock returns by using the recent multivariate GARCH model, namely the CCC of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003) and VARMA-AGARCH model of McAleer, et al. (2008). This paper investigates the WTI crude oil futures returns and stock returns of ten oil companies; which are composed of the "supermajor" group of oil companies, namely Exxon Mobil (XOM), Royal Dutch Shell (RDS), Chevron Corporation (CVX), ConocoPhillips (COP), BP (BP) and Total S.A. (TOT), and other large oil and gas companies in the world, namely Petrobras (PBRA), Lukoil (LKOH), Surgutneftegas (SNGS), and Eni S.p.A. (ENI). The empirical results present conditional correlation between WTI crude oil futures returns and very low returns in stock of the CCC model oil company. Surprisingly, for the VARMA-GARCH and VARMA-AGARCH models, no volatility spillover effects are observed in every pairs of return series. The paper also presents the evidence of asymmetric effect of negative and positive shock on conditional variance in every pairs of return series.