Problem
Suppose we have 4 points to fit a term structure: yields for a 2-year, 3-year, 5-year, and 7-year maturities. Let's consider the 3-year point. There are a bunch of ways to interpolate a term structure of interest rates.
• If we used cubic interpolation, does the 5y yield affect the value of the 3y yield? Provide 1 reason to support your answer.
• If we used cubic interpolation, does the 5y yield affect the slope at the 3y yield? Provide 1 reason to support your answer.