# How to Parameterize a Bond Yield Curve?

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)

• Search for Nelson-Siegel. However, I think most or all of these questions are off-topic for CV.
– The Laconic
Nov 26, 2018 at 21:31