ما معنى Monotone convex interpolation؟

Monotone convex interpolation (Hagan and West, 2006) builds the forward curve directly. On each interval it keeps the discrete forward $\bar f_j$, estimates the instantaneous forward $f_j$ at each pillar as the time-weighted average of the two adjacent discrete forwards, and fills the interval with $f(T)=\bar f_j + G(x)$, $x=(T-T_{j-1})/(T_j-T_{j-1})$, where $G$ is a quadratic, or a quadratic joined to a constant, with $G(0)=f_{j-1}-\bar f_j$, $G(1)=f_j-\bar f_j$ and $\int_0^1G=0$, chosen from four cases so that $G$ never overshoots its end values. The forward curve is continuous, reproduces every discrete forward, and stays within the range of the neighbouring forwards.