Additive normal tempered stable processes for equity derivatives and power-law scaling

We introduce a simple additive process for equity index derivatives. The model generalizes Lévy Normal Tempered Stable processes (e.g. NIG and VG) with time-dependent parameters. It accurately fits the volatility surfaces in whole time range of quoted instruments, including options small time-horizon (days) long (years). via its characteristic function. This allows using classical Fourier pricing techniques. discuss calibration issues detail we show that, terms mean squared error, is on average two orders magnitude better than both Sato alternatives. that even if loses stationarity property processes, it presents interesting scaling properties calibrated