Granger causality in risk and detection of extreme risk spillover between financial markets

Controlling and monitoring extreme downside market risk are important for financial risk management and portfolio/investment diversification. In this paper, we introduce a new concept of Granger causality in risk and propose a class of kernel-based tests to detect extreme downside risk spillover between financial markets, where risk is measured by the left tail of the distribution or equivalently by the Value at Risk (VaR). The proposed tests have a convenient asymptotic standard normal distribution under the null hypothesis of no Granger causality in risk. They check a large number of lags and thus can detect risk spillover that occurs with a time lag or that has weak spillover at each lag but carries over a very long distributional lag. Usually, tests using a large number of lags may have low power against alternatives of practical importance, due to the loss of a large number of degrees of freedom. Such power loss is fortunately alleviated for our tests because our kernel approach naturally discounts higher order lags, which is consistent with the stylized fact that today's financial markets are often more influenced by the recent events than the remote past events. A simulation study shows that the proposed tests have reasonable size and power against a variety of empirically plausible alternatives in finite samples, including the spillover from the dynamics in mean, variance, skewness and kurtosis respectively. In particular, nonuniform weighting delivers better power than uniform weighting and a Granger-type regression procedure. The proposed tests are useful in investigating large comovements between financial markets such as financial contagions. An application to the Eurodollar and Japanese Yen highlights the merits of our approach.