2020/11/09 by Beatrice Acciaio, Acciaio, Beatrice, Mathias Beiglboeck +3 · 1 citation
Economics, Econometrics and Finance · #Economic theories and models
paper · pdf · doi:10.48550/arxiv.2011.04274
We consider a model-independent pricing problem in a fixed-income market and\nshow that it leads to a weak optimal transport problem as introduced by Gozlan\net al. We use this to characterize the extremal models for the pricing of\ncaplets on the spot rate and to establish a first robust super-replication\nresult that is applicable to fixed-income markets.\n Notably, the weak transport problem exhibits a cost function which is\nnon-convex and thus not covered by the standard assumptions of the theory. In\nan independent section, we establish that weak transport problems for general\ncosts can be reduced to equivalent problems that do satisfy the convexity\nassumption, extending the scope of weak transport theory. This part could be of\nits own interest independent of our financial application, and is accessible to\nreaders who are not familiar with mathematical finance notations.\n