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

TL;DR

This paper applies weak optimal transport theory to model-independent pricing in fixed-income markets, addressing non-convex costs and establishing robust super-replication results with broader theoretical implications.

Contribution

It introduces a novel application of weak transport to fixed-income pricing and extends the theory to non-convex costs, broadening its mathematical scope.

Findings

Characterizes extremal models for caplet pricing.

Establishes a robust super-replication result.

Reduces non-convex weak transport problems to convex ones.

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.