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Weak Transport for Non-Convex Costs and Model-independence in a Fixed-Income Market

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  • Beatrice Acciaio
  • Mathias Beiglboeck
  • Gudmund Pammer

Abstract

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.

Suggested Citation

  • Beatrice Acciaio & Mathias Beiglboeck & Gudmund Pammer, 2020. "Weak Transport for Non-Convex Costs and Model-independence in a Fixed-Income Market," Papers 2011.04274, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2011.04274
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    References listed on IDEAS

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