Arbitrage bounds for the term structure of interest rates

Stefan R. Jaschke ()
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Stefan R. Jaschke: Institut fØr Mathematik, Humboldt-UniversitÄt zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

Finance and Stochastics, 1997, vol. 2, issue 1, 29-40

Abstract: 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 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, depending on the structure of transaction costs. 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.

Keywords: Term structure of interest rates; yield curve; arbitrage bounds; linear programming; duality theory; smoothing splines (search for similar items in EconPapers)
JEL-codes: C14 C61 E43 (search for similar items in EconPapers)
Date: 1997-11-13
Note: received: December 1995; final version received: May 1997 --> Abstract. 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 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, depending on the structure of transaction costs. 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.
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