Hi All,
Suppose I have a 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 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)
Thank you so much for your help!
All the best,
Kathy Chenying Gao
look at interest rate term structures.
my papers might provide a quick reference.
One accepted way is to use the semi parametric model from Nelsen where you can simply fit in values of B1 and B2 to find out the inflection points of the fitted curve.
For more analyzable phenomena beyond the graphical form you can either go for cochrane piazzesi factor which uses bond yields up to 5 years , here
http://leeds-faculty.colorado.edu/zender/Seminar/Spring2002/Piazzesi-Cochrane.pdf
You can also look at the work of Diebold et al, including this one: https://www.econstor.eu/bitstream/10419/25435/1/515150223.PDF
Here is another one using bond yields to tease out Currency and FX implications
https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/25782/Hodrick_Tomunen_Term%20Structure.NBERw25092.pdf
You can also use log functions and polynomial factorizations of the fitted curve to start off with your own analysis of the curve .
J'aimerais savoir le package qui sert à optimiser la fonction de Nelson Siegel avec 06 paramètres dans le langage R
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