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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 fixedincome 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.doi:10.1111/mafi.12328 fatcat:we3eg5zm3ndybitwgxejprrk4i