DRF.5F.tVar: Estimation of the De Rezende-Ferreira 5 Factor model's...

In DeRezende.Ferreira: Zero Coupon Yield Curve Modelling

Description

The command estimates the parameters of the De Rezende-Ferreira 5 Factor model using variable \ τ_{1} and \ τ_{2}

Usage

DRF.5F.tVar(rate, maturity)

Arguments

rate	Vector or matrix of class "zoo", which contains interest rates
maturity	Vector of class "numeric", wich contains the maturities

Details

The De Rezende-Ferreira model used to fit the forward rates is:

f_{t}≤ft(m\right) = β_{0t} + β_{1t} e^{-\frac{m}{τ_{1t}}} + β_{2t} e^{-\frac{m}{τ_{2t}}} + β_{3t} ≤ft ( {\frac{m}{τ_{1t}}} e^{-\frac{m}{τ_{1t}}} \right ) + β_{4t} ≤ft ( {\frac{m}{τ_{2t}}} e^{-\frac{m}{τ_{2t}}} \right )

The spot rates, derived from the forward rates f_{t}≤ft(m\right), are given by:

y_{t}≤ft ( m \right ) = β_{0t} + β_{1t} ≤ft (\frac{1 - e^{-\frac{m}{τ_{1t}}}}{\frac{m}{τ_{1t}}}\right) + β_{2t} ≤ft (\frac{1 - e^{-\frac{m}{τ_{2t}}}}{\frac{m}{τ_{2t}}}\right) + β_{3t} ≤ft (\frac{1 - e^{-\frac{m}{τ_{1t}}}}{\frac{m}{τ_{1t}}} - e^{-\frac{m}{τ_{1t}}}\right ) + β_{4t} ≤ft (\frac{1 - e^{-\frac{m}{τ_{2t}}}}{\frac{m}{τ_{2t}}} - e^{-\frac{m}{τ_{2t}}}\right )

The set of optimal parameters will be chosen according to the lowest RMSE value:

≤ft (\widehat{τ}_{1t},\widehat{τ}_{2t} \right) = argmin≤ft \{\frac{1}{N}∑_{t=1}^{N} √{\frac{1}{T}∑_{t=1}^{T}≤ft [ y_{t}≤ft (t_{n} \right ) - \widehat{y}_{t}≤ft (t_{n},τ_{1t}, τ_{2t},\widehat{β_{t}}\right )\right ]^{2} } \right \}

Value

An object of class "zoo", that contains \ ≤ft (β_{0t},\ β_{1t},\ β_{2t},\ β_{3t},\ β_{4t},\ τ_{1t},\ τ_{2t},\ SSR_{t},\ R^{2}_{t} \right)

Examples

#
# De Rezende-Ferreira 5F model on the Brazilian Data-Set
#

data(ZC_Brazil)
real.rate = ZC_Brazil

ZC_Brazil[["Date"]] = NULL

rate = zoo(ZC_Brazil)
index(rate) = as.POSIXct(paste(real.rate[["Date"]]))
maturity <- c(0.5, 0.75, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

RF.5F.Parameters <- DRF.5F.tVar(rate, maturity)

par(mfrow=c(3,2))
 plot(RF.5F.Parameters[,"beta0"],xlab="Date",ylab="BETA0",ylim=c(9.5,12.0),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta1"],xlab="Date",ylab="BETA1",ylim=c(-18.0,2.3),col= "blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta2"],xlab="Date",ylab="BETA2",ylim=c(-6.0,13.0),col= "blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta3"],xlab="Date",ylab="BETA3",ylim=c(-10.0,0.0),col= "blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta4"],xlab="Date",ylab="BETA4",ylim=c(-5.0,5.0),col="blue",lwd=1)
 grid(nx=12, ny=12)
par(mfrow=c(1,1))

par(mfrow=c(2,1))
 plot(RF.5F.Parameters[,"tau1"],xlab="Date",ylab="TAU1",ylim=c(0.2,1.3),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"tau2"],xlab="Date",ylab="TAU2",ylim=c(2.5,5.5),col="blue",lwd=1)
 grid(nx=12, ny=12)
par(mfrow=c(1,1))

#
# De Rezende-Ferreira 5F on the Russian Data-Set
#

data(ZC_Russia)
real.rate = ZC_Russia

ZC_Russia[["Date"]] = NULL

rate = zoo(ZC_Russia)
index(rate) = as.POSIXct(paste(real.rate[["Date"]]))
maturity <- c(0.25, 0.5, 0.75, 1,2,3,5,7,10,15,20,30)
RF.5F.Parameters <- DRF.5F.tVar(rate, maturity)

par(mfrow=c(3,2))
 plot(RF.5F.Parameters[,"beta0"],xlab="",ylab="BETA0",ylim=c(10.5,12.5),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta1"],xlab="Date",ylab="BETA1",ylim=c(-1.5,0.5),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta2"],xlab="Date",ylab="BETA2",ylim=c(-7.0,-3.5),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta3"],xlab="Date",ylab="BETA3",ylim=c(-1.5,3.5),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"beta4"],xlab="Date",ylab="BETA4",ylim=c(-5.5,-0.1),col="blue",lwd=1)
 grid(nx=12, ny=12)
par(mfrow=c(1,1))


par(mfrow=c(2,1))
 plot(RF.5F.Parameters[,"tau1"],xlab="Date",ylab="TAU1",ylim=c(0.1,1.9),col="blue",lwd=1)
 grid(nx=12, ny=12)
 plot(RF.5F.Parameters[,"tau2"],xlab="Date",ylab="TAU2",ylim=c(7.5,16.8),col="blue",lwd=1)
 grid(nx=12, ny=12)
par(mfrow=c(1,1))

DeRezende.Ferreira documentation built on May 2, 2019, 10:15 a.m.