Fast Fourier transform (FFT) method is now a standard calibration engine. However, in many situations, such as pricing of deep out-of-the-money European options, FFT produces large errors. We propose fast and accurate realizations of Integration-Along-Cut method (IAC method), which explicitly control the error of pricing OTM options. For one strike (and OTM options), IAC is significantly faster than FFT-based methods. Even if prices for many strikes are needed, IAC method, together with quadratic interpolation, successfully competes with CONV method developed by Lord et. al., the COS method suggested by Fang and Oosterlee, the saddlepoint method suggested by Carr and Madan, and the refined and enhanced versions of FFT recently suggested by M.~Boyarchenko and Levendorskii. For calculations of sensitivities, a relative advantage of IAC is even greater. The method is applicable to a wide class of Levy-driven models, KoBoL processes (a.k.a. CGMY model) of finite variation, Variance Gamma processes and Normal Inverse Gaussian processes including.