Price‐Admissibility Conditions for Arbitrage‐Free Linear Price Function Models for the Term Structure of Interest Rates

20 Pages Posted: 20 Sep 2016

See all articles by Andrew F. Siegel

Andrew F. Siegel

University of Washington - Department of Finance and Business Economics; National Bureau of Economic Research (NBER)

Date Written: October 2016

Abstract

To assure price admissibility — that all bond prices, yields, and forward rates remain positive — we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.

Keywords: term structure, interest rates, yields, bonds, linear price model

Suggested Citation

Siegel, Andrew F., Price‐Admissibility Conditions for Arbitrage‐Free Linear Price Function Models for the Term Structure of Interest Rates (October 2016). Mathematical Finance, Vol. 26, Issue 4, pp. 919-938, 2016, Available at SSRN: https://ssrn.com/abstract=2841041 or http://dx.doi.org/10.1111/mafi.12075

Andrew F. Siegel (Contact Author)

University of Washington - Department of Finance and Business Economics ( email )

Box 353200
Seattle, WA 98195
United States

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

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