Introduction to R for Quantitative Finance

Cubic spline regression

We need to choose the functions carefully if we want the estimation to yield a reasonably estimated discount function. The typical discount function is nonlinear. It is a monotonically decreasing function and converges to zero asymptotically at infinity. Thus, fitting a straight line is not a good idea. One can try to fit a higher order polynomial to the discount function. This is not a satisfactory solution either. If we fit low-order polynomials, they are usually not flexible enough and don't fit well, especially at the short-term maturities. If we fit high-order polynomials, they may fit well but tend to produce wild ...