  The computation of Greeks for exponential L\'evy models are usually
approached by Malliavin Calculus and other methods, as the Likelihood Ratio and
the finite difference method. In this paper we obtain exact formulas for Greeks
of European options based on the Lewis formula for the option value. Therefore,
it is possible to obtain accurate approximations using Fast Fourier Transform.
We will present an exhaustive development of Greeks for Call options. The error
is shown for all Greeks in the Black-Scholes model, where Greeks can be exactly
computed. Other models used in the literature are compared, such as the Merton
and Variance Gamma models. The presented formulas can reach desired accuracy
because our approach generates error only by approximation of the integral.
