Arbitrage Bounds of the Term Structure of Interest Rates

This paper proposes a methodology for simultaneously computing a smooth estimator of the term structure of interest rates and economically justified bounds for it. It unifies existing estimation procedures that apply regression, smoothing and linear programming methods. Our methodology adjusts for tax effects and (possibly asymmetric) transaction costs. Various regression and smoothing techniques have been suggested for estimating the term structure. They focus on what functional form to choose or which measure of smoothness to maximize, mostly neglecting the discussion of the appropriate measure of fit. Arbitrage theory provides insight into how small the pricing error will be and in which sense, given that arbitrage is restricted in a certain sense. We prove a general result relating the minimal pricing error one incurs in pricing all bonds with one term structure to the maximal arbitrage profit one can achieve with restricted portfolios. We give a compact review of the arbitrage theory of bond markets which is based on the duality theory of mathematical programming. Apart from term structure estimation, the theory can be used to optimize bond portfolios, spot arbitrage opportunities, and hedge non-traded cash flows