Svensson {YieldCurve} | R Documentation |
Returns the estimated coefficients of the Svensson's model.
Svensson(rate, maturity, Tau1 = c(3, 12), Tau2 = c(60, 120))
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 |
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]
Returns a data frame with the estimated coefficients: β_{0}, β_{1}, β_{2},β_{3}, λ_1 and λ_2.
Sergio Salvino Guirreri
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.
data(FedYieldCurve) tau <- c(3,6,12,60,84,120) A <- Svensson(FedYieldCurve[1:10,], tau, c(3,12), c(60,120) )