Yield Curve package R

Question

I want to interpolate a yield curve using Nelson-Siegel model. I'm new to R language but decided to use the "Yield Curve" package (available here http://cran.r-project.org/web/packages/YieldCurve/index.html and documentation's link: http://cran.r-project.org/web/packages/YieldCurve/YieldCurve.pdf ) There are 2 problems I faced:

1) I don't understand why the first 2 parameters of NSrates in the 6th and 7th line of the following code(p.6 in documentation) took that format:

data(FedYieldCurve)
tau <- c(3, 6, 12, 60, 84, 120)
mediumTerm <- c(12,60,84)
NSParameters <- Nelson.Siegel(rate=FedYieldCurve[1:10,],
                              maturity=tau, MidTau=mediumTerm )
y <- NSrates(NSParameters[5,1:3],
             NSParameters$lambda[5],tau)
plot(tau,FedYieldCurve[5,],main="Fitting Nelson-Siegel yield curve", type="o")
lines(tau,y, col=2)
legend("topleft",legend=c("observed yield curve","fitted yield curve"),
col=c(1,2),lty=1)
grid()

2) how to extract a certain yield from the curve? For example, If I have a maturity of 12 months, what is its related yield?.

Thank you a lot for taking time to answer my questions.

Answer 1

Look at the help page for NSrates .

It takes 3 arguments:

betaCoeff: vector or matrix of the beta's coefficients.

lambdat: value of the estimated lambda

maturity: maturity of the yield curve of which want to return the interest rates.

For betaCeff , the code you show uses NSParameters[5, 1:3] , or

   beta_0    beta_1   beta_2
5 13.7156 -1.468064 1.237194

which is a data.frame . Although data.frame is not explicitly stated as a possible input, the first line of the function converts it to a matrix (assuming you're using the CRAN version)

if(is.vector(betaCoeff)) betaCoeff <- matrix( betaCoeff, 1, 3)

For lambdat , the code you show uses NSParameters$lambda[5] which is the numeric value to use for the estimated lambda.

The final argument is maturity . The code you showed uses tau which is

> tau
[1]   3   6  12  60  84 120

Per the documentation, the function will

Return interest rates in matrix object with number of rows equal to nrow(betaCoeff) and number of columns equal to length(maturity).

In this case, you get

> y
           3        6       12      60       84      120
[1,] 12.7394 13.05852 13.40245 13.6897 13.69721 13.70273

If you only want the 12 month maturity , then pass only 12 to the maturity argument.

> NSrates(NSParameters[5,1:3], NSParameters$lambda[5], 12)
           12
[1,] 13.40245