🤖 AI Summary
This paper addresses static fixed-income pricing and liability cash-flow replication by developing a model-free no-arbitrage framework. Methodologically, it rigorously establishes that static no-arbitrage is equivalent to the existence of a strictly positive discount curve that exactly reproduces all market quotes; integrates static arbitrage analysis, convex optimization, and measure-theoretic pricing; and systematically studies exact and super-replication of liabilities. Key contributions include: (i) the first necessary and sufficient condition for the existence of a minimum-cost super-replicating portfolio; and (ii) the first rigorous theoretical foundation for static swap–repo replication. The framework unifies discount-curve construction with liability-driven investing, thereby enhancing robustness, interpretability, and operational feasibility in liability matching—directly supporting economic capital calculation and regulatory practice. (149 words)
📝 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.