Advanced Curve Construction: Interpolation Techniques

Apply linear interpolation to a discrete spot rate curve and analyze its primary drawback: discontinuous forward rates.

Apply polynomial interpolation and identify its potential for instability and oscillations (Runge's phenomenon).

Explain the mathematical intuition of cubic splines for creating smooth, continuous yield and forward rate curves.

Implement cubic spline interpolation in Python to fit a continuous curve to bootstrapped spot rates.

Compare the spot and forward curves generated by linear, polynomial, and spline interpolation methods.