Volatility conditional on price trends
  The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by trend'' constitutes a new stylized fact. The past price behaviour is measured by a product of 2 non overlapping returns, of the form r L[r] where L is the lag operator. The effect is studied empirically using USD/CHF foreign exchange data, in a large range of time horizons. A set of ARCH based processes are modified in order to include the trend effect, and their forecasting performances are compared. For a better forecast, it is shown that the main factor is the shape of the memory kernel (i.e. power law), and the following factor is the inclusion of the trend effect. 
Gilles Zumbach