The problem of statically hedging European options of shorter maturity by using longer maturity vanilla options is studied in this paper. This question is important, e.g., when analysing options on forwards in relation to liquid options on the underlying spot, the price of which is modelled as an exponential additive process under a risk-neutral measure. Fourier transform techniques are the key to solving the hedging problem. Under mild smoothness and integrability assumptions on the payoff function \(p\), the authors show the existence of feasible hedging strategies involving European calls that converge (in \(L^1\) and almost surely) to the payoff \(p\). Practically important questions of using only finitely many hedging instruments and dealing with cases when the payoff function \(p\) does not satisfy the needed integrability conditions are discussed next. Here, the authors rely on Tichonov regularisation and numerical integration via Gaussian quadrature. Finally, the obtained results are extensively illustrated on the standard Black-Scholes-Merton (BSM), Carr-Geman-Madan-Yor (CGMY) and Heston asset price process models. Parameter choices, the quality of the obtained hedges, and differences between static and dynamic hedging are explained.