Fixed-Income Pricing and the Replication of Liabilities

Abstract

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. The absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve reproducing all observed prices. Linear programming duality then identifies the least-cost super-replication price with the largest value that any admissible discount curve assigns to the liability, so that the resulting bounds are attained and cannot be improved. Complementary slackness confines over-replication to dates that the optimal discount vector prices at zero, and a least-cost portfolio matches the liability exactly at no fewer dates than the rank of the cash-flow matrix. We also obtain generic uniqueness of that portfolio, an interpolation between quadratic hedging and super-replication, and a static treatment of swap--repo strategies. On US Treasury cross-sections the observed prices violate the law of one price, so that a discount curve must be estimated rather than bootstrapped; the least-cost portfolio then matches an annuity liability at almost every cash-flow date.