  In this paper we investigate a class of swing options with firm constraints
in view of the modeling of supply agreements. We show, for a fully general
payoff process, that the premium, solution to a stochastic control problem, is
concave and piecewise affine as a function of the global constraints of the
contract. The existence of bang-bang optimal controls is established for a set
of constraints which generates by affinity the whole premium function. When the
payoff process is driven by an underlying Markov process, we propose a
quantization based recursive backward procedure to price these contracts. A
priori error bounds are established, uniformly with respect to the global
constraints.
