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#### Example 1.1: Bootstrapping zero rates
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# Defining cash flow of the bonds
T <- 241+3*365
bond.A <- 0*c(1:T)
bond.A[190] <- 100
bond.B <-  0*c(1:T)
bond.B[32] <- 5.5
bond.B[32+365] <- 5.5
bond.B[32+2*365] <- 105.5
bond.C <- 0*c(1:T)
bond.C[241] <- 6.75
bond.C[241+365] <- 6.75
bond.C[241+2*365] <- 6.75
bond.C[241+3*365] <- 106.75

# Plotting the cash flow of the three bonds
tvec <- c(1:T)/365
plot(tvec,bond.A,type="h", ylim=c(0,110), lty="solid", xlab="",ylab="")
par(new = TRUE)
plot(tvec,bond.B,type="h", lty="longdash",ylim=c(0,110), xlab="",ylab="")
par(new = TRUE)
plot(tvec,bond.C,type="h", lty="dotted",ylim=c(0,110), xlab="",ylab="")
points(tvec[190],bond.A[190],pch=21)
points(tvec[32],bond.B[32],pch=22)
points(tvec[32+365],bond.B[32+365],pch=22)
points(tvec[32+2*365],bond.B[32+2*365],pch=22)
points(tvec[241],bond.C[241],pch=24)
points(tvec[241+365],bond.C[241+365],pch=24)
points(tvec[241+2*365],bond.C[241+2*365],pch=24)
points(tvec[241+3*365],bond.C[241+3*365],pch=24)

###
#  Bootstrapping
###

# Define the time vector (numbers in book are rounded)
tvec<-c((24+8)/365,(24+31+30+31+31+28+15)/365,(24+31+30+31+31+28+31+30+5)/365,(24+8+365)/365,(24+31+30+31+31+28+31+30+5+365)/365,(24+8+365+365)/365,(24+31+30+31+31+28+31+30+5+365+365)/365,(24+31+30+31+31+28+31+30+5+365+365+365)/365)

# Perform bootstrapping 
discvec<-tvec
# Start with d2
discvec[2]<-99.65/100
# Find d1 by linear interpolation
discvec[1]<-1+(discvec[2]-1)/(tvec[2]-0)*(tvec[1]-0)
# Find d6 and using linear interpolation for d4
discvec[6]<-(113.43-5.5*discvec[1]-5.5*discvec[2]*(1-(tvec[4]-tvec[2])/(tvec[6]-tvec[2])))/(5.5*(tvec[4]-tvec[2])/(tvec[6]-tvec[2])+105.5)
# Find d3,d4, and d5 by linear interpolation
discvec[3]<-discvec[2]+(discvec[6]-discvec[2])/(tvec[6]-tvec[2])*(tvec[3]-tvec[2])
discvec[4]<-discvec[2]+(discvec[6]-discvec[2])/(tvec[6]-tvec[2])*(tvec[4]-tvec[2])
discvec[5]<-discvec[2]+(discvec[6]-discvec[2])/(tvec[6]-tvec[2])*(tvec[5]-tvec[2])
# Find d8 using linear interpolation for d7
discvec[8]<-(121.3-6.75*discvec[3]-6.75*discvec[5]-6.75*discvec[6]*(1-(tvec[7]-tvec[6])/(tvec[8]-tvec[6])))/(6.75*(tvec[7]-tvec[6])/(tvec[8]-tvec[6])+106.75)
# Find d7 by linear interpolation
discvec[7]<-discvec[6]+(discvec[8]-discvec[6])/(tvec[8]-tvec[6])*(tvec[7]-tvec[6])
# The resulting discount factors
discvec
plot(tvec,discvec,type="l")
points(tvec,discvec)
# The corresponding zero rates
zerorates <- (-1)*log(discvec)/tvec
zerorates
plot(tvec,zerorates,type="l")
points(tvec,zerorates)