Fixed-Income Pricing and the Replication of Liabilities

TL;DR

This paper introduces a model-free, static framework for fixed-income pricing and liability replication, linking arbitrage absence to a positive discount curve that matches market prices, with implications for risk management and regulation.

Contribution

It develops a unified, model-free approach to fixed-income valuation and liability replication, including conditions for super-replication and a rigorous interpretation of swap--repo strategies.

Findings

Absence of static arbitrage implies a positive discount curve.

Conditions for least-cost super-replication are established.

Framework applies to economic capital and regulatory practices.

Abstract

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. We show that the absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve that reproduces all observed market prices. We then study the replication and super-replication of liabilities and establish conditions ensuring the existence of least-cost super-replicating portfolios, including a rigorous interpretation of swap--repo replication within this static framework. The results provide a unified foundation for discount-curve construction and liability-driven investment, with direct relevance for economic capital assessment and regulatory practice.