Interest Rate Term Structure Estimation with Exponential Splines: A Note



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    • Economist, International Finance Division, Federal Reserve Board. This paper reflects the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. Computational assistance was given by David Laughton and John Davison. J. Huston McCulloch alsomadeanumberofhelpfulsuggestionsonmatterscoveredinthispaper. Kathy Krasney ably typed the manuscript and its revisions.


Vasicek and Fong [11] developed exponential spline functions as models of the interest rate term structure and claim such models are superior to polynomial spline models. It is found empirically that i) exponential spline term structure estimates are no more stable than estimates from a polynomial spline model, ii) data transformations implicit in the exponential spline model frequently condition the data so that it is difficult to obtain approximations in which one can place confidence, and iii) the asymptotic properties of the exponential spline model frequently are unrealistic. Estimation with exponential splines is no more convenient than estimation with polynomial splines and gives substantially identical estimates of the interest rate term structure as well.