Options on several underlyings are a common exotic product in the equity and FX derivatives market. The value of these kinds of options also depends on the correlation of the underlyings. We will present a model to compute a lower bound for the price of this option. The model, represented by a non-linear parabolic PDE, is implemented with finite elements in order to be able to compute accurate cross-derivatives We will demonstrate the results with several derivatives from the European market.