The paper considers the problem of volatility co-movement, namely as to whether two financial returns have perfectly correlated common volatility process, in the framework of multivariate stochastic volatility models and proposes a test which checks the volatility co-movement. The proposed test is a stochastic volatility version of the co-movement test proposed by Engle and Susmel (1993), who investigated whether international equity markets have volatility co-movement using the framework of the ARCH model.

In empirical analysis we found that volatility co-movement exists among closely-linked stock markets and that volatility co-movement of the exchange rate markets tends to be found when the overall volatility level is low, which is contrasting to the often-cited finding in the financial contagion literature that financial returns have co-movement in the level during the financial crisis.