Which of the following is a required property of the cubic spline approach to estimating the yield curve and discount functions $d ( t )$ ? Recall that the approach fits functions $d _ { k } ( t )$ to $k$ regions between $( k + 1 )$ knot points. A) $d ( 0 ) 1$ B) $d _ { k } \left( T _ { k + 1 } \right) = d _ { k + 1 } \left( T _ { k + 1 } \right)$ C) $d _ { k } ^ { \prime } \left( T _ { k + 1 } \right) d _ { k + 1 } ^ { \prime } \left( T _ { k + 1 } \right)$ D) $d _ { k } ^ { \prime \prime } \left( T _ { k + 1 } \right)

Question

Which of the following is a required property of the cubic spline approach to estimating the yield curve and discount functions $d ( t )$ ? Recall that the approach fits functions $d _ { k } ( t )$ to $k$ regions between $( k + 1 )$ knot points.
A) $d ( 0 ) > 1$
B) $d _ { k } \left( T _ { k + 1 } \right) = d _ { k + 1 } \left( T _ { k + 1 } \right)$
C) $d _ { k } ^ { \prime } \left( T _ { k + 1 } \right) > d _ { k + 1 } ^ { \prime } \left( T _ { k + 1 } \right)$
D) $d _ { k } ^ { \prime \prime } \left( T _ { k + 1 } \right) < d _ { k + 1 } ^ { \prime \prime } \left( T _ { k + 1 } \right)$ where $d ^ { \prime } ( t )$ and $d ^ { \prime \prime } ( t )$ denote first and second derivatives of the function $d ( t )$ with respect to $t$ .

Quizplus · Accepted Answer

The cubic spline approach requires that the functions $d_k(t)$ for adjacent regions are continuous at the knot points. This means that the value of $d_k(t)$ at the end of one region ($T_{k+1}$) must equal the value of $d_{k+1}(t)$ at the start of the next region, ensuring a smooth transition between spline segments.

Which of the Following Is a Required Property of the Cubic