  We study valuation of swing options on commodity markets when the commodity
prices are driven by multiple factors. The factors are modeled as diffusion
processes driven by a multidimensional L\'evy process. We set up a valuation
model in terms of a dynamic programming problem where the option can be
exercised continuously in time. Here, the number of swing rights is given by a
total volume constraint. We analyze some general properties of the model and
study the solution by analyzing the associated HJB-equation. Furthermore, we
discuss the issues caused by the multi-dimensionality of the commodity price
model. The results are illustrated numerically with three explicit examples.
