Suppose I have a Bond Yield Curve (assume Semi-Annual Compounding), at term 1M, 3M... 1Y, 2Y... 10Y, 15Y ...30Y (x-axis is maturity / term).
How should I parameterize this yield curve? Any recommendations? Is there any known formula of Yield as a function of Maturity (or any approximations)?
And I also have some questions about the property of this yield curve:
First of all, is yield curve (strictly) monotone increase? Does the first order derivative have any meaning?
Secondly, does yield curve has an asymptote, as x -> Inf, y -> constant? Is the y-values bounded by a lower bound when x=0?
Thirdly, what can we say about the second order derivative f''? Does f'' has an upper-bound? Should the f'' be strictly non-negative? Or should we expect f'' change sign? If f'' did change sign, what does it tell us?
Finally, does the Area-Under-Curve has any meaning? (like those ROC curve has a meaningful AUC)