  We consider a model-independent pricing problem in a fixed-income market and
show that it leads to a weak optimal transport problem as introduced by Gozlan
et al. We use this to characterize the extremal models for the pricing of
caplets on the spot rate and to establish a first robust super-replication
result that is applicable to fixed-income markets.
  Notably, the weak transport problem exhibits a cost function which is
non-convex and thus not covered by the standard assumptions of the theory. In
an independent section, we establish that weak transport problems for general
costs can be reduced to equivalent problems that do satisfy the convexity
assumption, extending the scope of weak transport theory. This part could be of
its own interest independent of our financial application, and is accessible to
readers who are not familiar with mathematical finance notations.
