Consistent pricing of bivariate interest rate exotics via constrained Schrödinger optimal transport

2026-07-17

AI Summary

This study addresses the pricing inconsistency between bivariate interest rate exotic derivatives—such as CMS spread options—and their two underlying CMS options observed in the market. To resolve this, the authors develop a unified arbitrage-free pricing framework by formulating and solving the dual Lagrangian of a constrained Schrödinger optimal transport problem. This work represents the first application of constrained optimal transport theory to achieve cross-market consistency in interest rate derivative pricing. The proposed framework guarantees that the prices of exotic instruments remain compatible with observable market data while efficiently computing their no-arbitrage price bounds. Numerical experiments demonstrate the method’s practical feasibility, robustness, and computational efficiency in real-world pricing scenarios.

Abstract

We develop a modeling framework for pricing bivariate interest rate exotic derivatives that maintains consistency across three interconnected markets: CMS spread options and the two underlying CMS option markets that define the spread. Our approach also enables the computation of no-arbitrage bounds for exotic derivatives given observable market prices in the spread option and underlying CMS option markets. The method relies on solving the dual Lagrangian of a constrained version of the Shrödinger optimal transport problem and we demonstrate the practical applicability of our framework through concrete numerical examples that illustrate both the pricing methodology and the computation of no-arbitrage bounds. The approach offers a robust tool for pricing complex interest rate derivatives while ensuring consistency with liquid market instruments.

Problem

• bivariate interest rate exotics
• price consistency
• CMS spread options
• no-arbitrage bounds
• market consistency

Innovation

• constrained Schrödinger optimal transport
• bivariate interest rate exotics
• no-arbitrage bounds
• CMS spread options
• dual Lagrangian formulation