  This paper examines quantile dependence between international stock markets
and evaluates its use for improving volatility forecasting. First, we analyze
quantile dependence and directional predictability between the US stock market
and stock markets in the UK, Germany, France and Japan. We use the
cross-quantilogram, which is a correlation statistic of quantile hit processes.
The detailed dependence between stock markets depends on specific quantile
ranges and this dependence is generally asymmetric; the negative spillover
effect is stronger than the positive spillover effect and there exists strong
directional predictability from the US market to the UK, Germany, France and
Japan markets. Second, we consider a simple quantile-augmented volatility model
that accommodates the quantile dependence and directional predictability
between the US market and these other markets. The quantile-augmented
volatility model provides superior in-sample and out-of-sample volatility
forecasts.
