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I have question about the linear interpolation of interest rates. I am unable to reconcile the Bloomberg methodology for calculating risk-free rate between maturities. In theory it is a straight-line interpolation, but the numbers don't pan out.

For example,

2 year US Sovereign Strips Yield: 0.333%(BEY)

3 year US Sovereign Strips Yield: 0.633%(BEY)

According to the straight-line method the Yield for 2.826 year is 0.5808%(BEY)

While the interpolated 2.826 year Yield is 0.619% from Blg interpolation function(BEY)

in addition, the additional information is below

1 year US Sovereign Strips Yield: 0.11%(BEY)

2 year US Sovereign Strips Yield: 0.333%(BEY)

3 year US Sovereign Strips Yield: 0.633%(BEY)

4 year US Sovereign Strips Yield: 1.058%(BEY)

5 year US Sovereign Strips Yield: 1.426%(BEY)

Is there anyone can calibrate the result from blg?

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They may interpolate based on actual issues closer to the target date than the 2 or 3 year... –  assylias Dec 13 '13 at 11:30
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This question appears to be off-topic because it is a question the data vendor can answer. –  Joshua Ulrich Dec 22 '13 at 18:09
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1 Answer

I don't think a linear interpolation is performed. The fact that the interpolated value is higher than a linear model suggest a concave function. I performed an experiment with the Nelson-Siegel interpolation model using your data. I put the data in a csv file and ran the following code (Book2.csv) is my data and the exercise was performed on R

library('YieldCurve')
a <- read.csv("../Book2.csv")
matur <- a[,1]
rate.corporate <- t(matrix(a[, 2], dimnames = list(paste("M", c(1:dim(a)[1])) ,"2013-11-    18")))
r.corp.xts <- as.xts(rate.corporate, descr='xts from matrix')
NSpars <- Nelson.Siegel(rate=r.corp.xts, maturity=matur)
NSrates(NSpars,2.826)

And the answer was 5.905% which is still short of the 6+% answer that bloomberg gives you, but higher than linear.

So you just have to find out what methodology is used by bloomberg. Cubic splines, nelson-siegel, etc.

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