Capturing Non-Linearity in the Term Structure of Interest Rates: A Fuzzy Logic Method of Estimating the Yield Curve

This paper provides a new solution to the problem of estimating the yield curve from a sample of coupon bonds. Our approach builds on the work of McMulloch (1971, 1975) by using a new approach to formulate and estimate the discount function for US Government Issue Coupon Bonds. This new method uses fuzzy regression to estimate an arbitrary nonlinear function, rather than estimating a polynomial specification, after using fuzzy clustering to break the bond sample into various clusters based on term to maturity. Estimates from the fuzzy regression are used to calculate the discount function, yield curve and the theoretical prices for the in-sample securities. Finally, estimates of the standard errors of the yield curve, discount function, price estimates, and forward curves can be obtained by bootstrapping. Our fuzzy analysis provides a very flexible way of dealing with the inherent nonlinearities in the problem, without imposing an arbitrary functional form and it provides some encouraging results for the data that have been analyzed to date.