termstrc (version 1.1.1)

nelson_estim: Zero-coupon Yield Curve Estimation with the Nelson/Siegel, Svensson Method

Description

Zero-coupon yield curve estimation with the parametric Nelson and Siegel (1987) method and the Svensson (1994) extension.

Usage

nelson_estim(group,
             bonddata,
             matrange = "all",
             method = "Nelson/Siegel",
             fit = "prices",
             weights = "duration",
             startparam,
             control = list(eval.max = 1000, iter.max= 500))

Arguments

group

vector defining the group of bonds used for the estimation, e.g. c("GERMANY","AUSTRIA").

bonddata

a data set of bonds in list format.

matrange

use "all" for no restrictions, or restrict the maturity range used for the estimation with c(lower,upper).

method

"Nelson/Siegel" or "Svensson".

fit

use "prices" ("yields") for minimizing the squared pricing (yield) errors.

weights

weighting of the errors used in the optimization ("none" or "duration").

startparam

matrix of start parameters, for the Nelson/Siegel (Svensson) method 4 (6) parameters for each each group are required (one row per group).

control

list of control parameters for the function nlminb().

Value

• The function nelson_estim returns an object of the class "nelson". The object contains the following items (mainly lists):
• group
  group of bonds (e.g. countries) used for the estimation.
• matrange
  "none" or a vector with the maturity range.
• method
  estimation method ("Nelson/Siegel" or "Svensson").
• fit
  objective function ("prices", or "yields").
• weights
  weighting of the errors used in the optimization ("none" or "duration").
• n_group
  length of object group, i.e. the number of countries.
• spot
  zero-coupon yield curves as object of the class "spot_curves".
• spread
  spread curves as object of the class "s_curves".
• forward
  forward curves as object of the class "fwr_curves".
• discount
  discount curves as object of the class "df_curves".
• expoints
  extrapolation points for Nelson/Siegel method.
• cf
  cashflow matrices.
• m
  maturity matrices.
• p
  dirty prices.
• phat
  estimated bond prices.
• perrors
  pricing errors and maturities as object of the class "error".
• y
  bond yields.
• yhat
  one list for each group with the theoretical bond yields calculated with the estimated bond prices phat.
• yerrors
  yield errors and maturities as object of the class "error".
• opt_result
  optimization results from nlminb, e.g. optimal parameters, convergence info.

Details

• group

{The first element of the vector will be used as the reference country for the spread curve calculation. group can be either a vector of bond groups or a scalar.} bonddata{The package is designed to work with a certain list data structure. For more information use the function str() to explore the structure of the example data sets.}

startparam{A matrix of start parameters must be provided for the estimation. Due to the possible existence of multiple local minima, a great effort should be invested in finding a good start parameter set. For rolling estimation procedures, the previous optimal parameters should be used as inputs for the next iteration.}

control{Please refer to the documentation of the function nlminb.}

References

Charles R. Nelson and Andrew F. Siegel (1987): Parsimonious Modeling of Yield Curves. The Journal of Business, 60(4):473--489.

Lars E.O. Svensson (1994): Estimating and Interpreting Forward Interest Rates: Sweden 1992 -1994. Technical Reports 4871, National Bureau of Economic Research.

See Also

print.nelson, summary.nelson, plot.nelson, splines_estim, plot.spot_curves, plot.s_curves, plot.df_curves, plot.fwr_curves, plot.error, uniroot.

Examples

# load data set
data(eurobonds)

# define countries, for which the estimation 
# of the zero-coupon yield curves will be carried out
group <- c("GERMANY", "AUSTRIA", "ITALY")

# define data set
bonddata <- eurobonds

# set maturity range
matrange <- c(2,12)

# define the used method
method <- "Nelson/Siegel"

# the weighted squared price errors will be minimized
fit <- "prices"
weights <- "duration"

# naive start parameters
b <- matrix(rep(c(0,0,0, 1),3),nrow=3,byrow=TRUE)
rownames(b) <- group
colnames(b) <- c("beta0","beta1","beta2","tau1")

# perform estimation
x <- nelson_estim(group, bonddata, matrange, 
                  method, fit, weights, startparam=b)

# prints the obtained parameters of the estimation
print(x)

# goodness of fit measures
summary(x)

# plots the zero-coupon yield curves for each country 
plot(x,errors="none")

# plots all zero-coupon yield curves togther
plot(x,multiple=TRUE, errors="none")

# spread curve splot
plot(x,ctype="spread",errors="none")

# price error plot for all countries
plot(x,ctype="none")