Constrained smoothing -splines for the term structure of interest rates

The constrained smoothing B-splines (COBS) is proposed as a nonparametric approach to estimate the term structure of interest rate. Compared to the existing methods in the literature, COBS’ main innovation lies in its incorporation of important constraints imposed by no-arbitrage, such as monotonically decreasing and boundary conditions for the discount function, positive forward and spot rates. In addition, by estimating the conditional median function, COBS is less sensible to outliers in reduced samples than other common methods in the literature. Estimation for high and low liquidity markets together with simulation exercises puts COBS in an intermediate position between usual parametric and nonparametric methods in the literature. It has more flexibility than parametric methods and, compared to other nonparametric methods, satisfies no-arbitrage constraints and generates parsimonious shapes of the term structure of interest rates.