Estimating Term Structure Using Nonlinear Splines: A Penalized Likelihood Approach 1

The spline-based models are widely used in practice to estimate the term structure of interest rates from a set of observed coupon-bond prices. The most popular method can be traced back to McCulloch (1971). Assuming that the price of a bond is equal to the present value of its future coupon payments and redemption, cash flows are regressed on a set of basis functions to estimate discount functions. Once the discount function is estimated, the zerocoupon yield and the forward rate can be obtained by transformations of the discount function. Though this method was followed by a lot of researchers, some serious drawbacks have been reported. The most important problem is the instability of estimated yield curves. As is widely known