Book excerpt: This paper examines volatility spillovers from mature to emerging stock markets and tests for changes in the transmission mechanism-contagion-during turbulences in mature markets. Tri-variate GARCH-BEKK models of returns in global (mature), regional, and local markets are estimated for 41 emerging market economies (EMEs), with a dummy capturing parameter shifts during turbulent episodes. LR tests suggest that mature markets influence conditional variances in many emerging markets. Moreover, spillover parameters change during turbulent episodes. Conditional variances in most EMEs rise during these episodes, but there is only limited evidence of shifts in conditional correlations between mature and emerging markets.