  We introduce a simple model for equity index derivatives. The model
generalizes well known L\`evy Normal Tempered Stable processes (e.g. NIG and
VG) with time dependent parameters. It accurately fits Equity index implied
volatility surfaces in the whole time range of quoted instruments, including
small time horizon (few days) and long time horizon options (years). We prove
that the model is an Additive process that is constructed using an Additive
subordinator. This allows us to use classical L\`evy-type pricing techniques.
We discuss the calibration issues in detail and we show that, in terms of mean
squared error, calibration is on average two orders of magnitude better than
both L\`evy processes and Self-similar alternatives. We show that even if the
model loses the classical stationarity property of L\`evy processes, it
presents interesting scaling properties for the calibrated parameters.
