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Consider a semi-annual coupon bond. Its face value is $1,000, it bears a 6 percent coupon rate per year, and will mature in 2 years.
Maturity
Spot Rates
Forward Rates
0.5
0.9
f1= f(0,0.5)
1.0
1.3
f2 = f(0.5,1)
1.5
1.8
f3 = f(1,1.5)
2.0
2.3
f4 = f(1.5, 2)
Compute the bond price using the sport rates. The bond equation is:
Where Zt represent a zero rate at time t and Ct is a cash flow at time t.
2) Calculate the respective implied forward rates from the corresponding spot rates.
3) Calculate the bond price using the implied forward rates using the following equation.
4) Suppose that the CIR model generates the following binomial interest tree (forward rates) lattice. Calculate the bond price using the backward induction method.
t=1
t=2
t=3
t=4
0.90
2.2
4.9
8.7
2.8
5.0
1.6
2.9
1.7
5) Check whether the bond price from 3) is the same as the bond price from 2).
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