varphi_X(u) = mathbbE[e^iuX] — the Fourier transform of the density. Exists for every distribution (unlike the MGF) and determines it uniquely (Lévy's inversion theorem). For Lévy processes the Lévy-Khintchine representation gives varphi in closed form, which is why Fourier pricing (Carr-Madan FFT) is the workhorse for affine models (Heston, VG, CGMY, Merton jump-diffusion) where the density has no closed form but varphi does.