Why Bloomberg Yield Interpolation May Differ from a Straight Line
Summary
The document asks why Bloomberg’s interpolated US Treasury STRIPS yield at an intermediate maturity does not match a straight-line calculation between the quoted two- and three-year yields. It gives yields from one through five years and reports that the Bloomberg value is higher than the linear estimate. The exchange does not identify Bloomberg’s actual curve construction method or calibrate its output.
Replies suggest that the interpolation may be nonlinear, mentioning cubic splines and Nelson–Siegel as possibilities. One respondent tests Nelson–Siegel on the supplied observations, but the resulting estimate still does not match the reported Bloomberg figure. Another cautions that the compared rates might come from different curve types or underlyings, and that STRIPS quotes may reflect actively traded securities. The examples illustrate why matching the instrument, curve definition, and methodology matters before comparing interpolated rates. The proposed alternatives are speculation and an exploratory test, not evidence of Bloomberg’s specific implementation.
Key ideas
- A straight-line yield estimate may differ from a vendor’s interpolated curve value.
- The replies do not establish which interpolation method Bloomberg uses.
- Nelson–Siegel is tested as an example, but its estimate does not reproduce the reported value.
- Curve type, underlying instrument, and quoted STRIPS data may affect comparisons.
Tags
Full text
# Bloomberg interest rate interpolation
# Bloomberg interest rate interpolation
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?
## Answer by JoshK (score 1)
https://quant.stackexchange.com/a/25154
Go through the docs, they have something on how they interpolate the curve. It's definitely not linear. AND remember, they have many different types of curves with different underlyings so you could be looking at a swap curve and comparing to a TSY curve and you will be off.
## Answer by Wilmer E. Henao (score 0)
https://quant.stackexchange.com/a/9947
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.
## Answer by Helin (score 0)
https://quant.stackexchange.com/a/12647
I don't have access to BBG right now, but are you sure these are not straight quoted STRIPS yields? Coupon & principal STRIPS are relatively actively traded in the US and these may just be generic STRIPS yields.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.