You are given two discount bonds of one-year and two-year maturities,with prices of 95 and 90,respectively.A third bond of three-year maturity and an annual coupon of 8% is trading at par.What is the three-year continuously-compounded zero-coupon rate?

Question

Quizplus · Accepted Answer

We first find the three-year discount function using matrix bootstrapping (see the chapter appendix).Then we convert the discount function in a zero-coupon rate.The calculations are as follows:
> C = matrix(c(100,0,8,0,100,8,0,0,108),3,3)
> C
[,1] [,2] [,3]
[1,] 100 0 0
[2,] 0 100 0
[3,] 8 8 108
> P = matrix(c(95,90,100),3,1)
> P
[,1]
[1,] 95
[2,] 90
[3,] 100
> d = solve(C)%*% P
> d
[,1]
[1,] 0.9500000
[2,] 0.9000000
[3,] 0.7888889
> z3 = (-1/3)*log(d[3])
> z3
[1] 0.07904326

You Are Given Two Discount Bonds of One-Year and Two-Year