Svensson {YieldCurve}R Documentation

Estimation of the Svensson parameters

Description

Returns the estimated coefficients of the Svensson's model.

Usage

Svensson(rate, maturity, Tau1 = c(3, 12), Tau2 = c(60, 120))

Arguments

rate vector or matrix which contains the interest rates.
maturity vector wich contains the maturity ( in months) of the rate. The vector's length must be the same of the number of columns of the rate.
Tau1 vector of short-term maturity
Tau2 vector of long-term maturity

Details

The Svensson's model to describe the forward rate is:

y_t(tau) = β_{0} + β_{1} exp( -frac{tau}{λ_1} ) + β_2 frac{tau}{λ_1} exp ( -frac{tau}{λ_1} ) + β_3 frac{tau}{λ_2} exp ( -frac{tau}{λ_2} )

The spot rate can be derived from forward rate and it is given by:

y_t(tau) = β_0 + β_1 frac{ 1- exp( -frac{tau}{λ_1}) }{frac{tau}{λ_1} } + β_2 <=ft[frac{ 1- exp( -frac{tau}{λ_1}) }{frac{tau}{λ_1} } - exp( -frac{tau}{λ_1}) right] + β_3 <=ft[frac{ 1- exp(-frac{tau}{λ_2}) }{frac{tau}{λ_2} } - exp( -frac{tau}{λ_2}) right]

Value

Returns a data frame with the estimated coefficients: β_{0}, β_{1}, β_{2},β_{3}, λ_1 and λ_2.

Author(s)

Sergio Salvino Guirreri

References

Svensson, L.E. (1994), Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994, IMF Working Paper, WP/94/114.

Nelson, C.R., and A.F. Siegel (1987), Parsimonious Modeling of Yield Curve, The Journal of Business, 60, 473-489.

Examples

data(FedYieldCurve)
tau <- c(3,6,12,60,84,120)
A <- Svensson(FedYieldCurve[1:10,], tau, c(3,12), c(60,120) )

[Package YieldCurve version 2.0 Index]