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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 8Term Structure Modeling Using Exponential Splines

By Oldrich A. Vasicek and H. Gifford Fong

Journal of Finance 37, No. 2, 339–348, 1982; reprinted in Dynamic Asset-Pricing Models, A.W. Lo (ed.), Cheltenham, G.B.: Edward Elgar Publishing Ltd., 2007.

Introduction

Term structure of interest rates provides a characterization of interest rates as a function of maturity. It facilitates the analysis of rates and yields such as discussed in Dobson, Sutch, and Vanderford [1976], and provides the basis for investigation of portfolio returns as for example in Fisher and Weil [1971]. Term structure can be used in pricing of fixed-income securities (cf., for instance, Houglet [1980]), and for valuation of futures contracts and contingent claims, as in Brennan and Schwartz [1977]. It finds applications in analysis of the effect of taxation on bond yields (cf. McCulloch [1975a] and Schaefer 1981), estimation of liquidity premia (cf. McCulloch [1975b]), and assessment of the accuracy of market-implicit forecasts (Fama [1976]). Because of its numerous uses, estimation of the term structure has received considerable attention from researchers and practitioners alike.

A number of theoretical equilibrium models has been proposed in the recent past to describe the term structure of interest rates, such as Vasicek [1977] (Chapter 6 of this volume), Brennan and Schwartz [1979], Langetieg [1980], and Cox, Ingersoll, and Ross [1981]. These models postulate alternative assumptions about the ...

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