Fixed Income

Question 1

a. 5-year spot rate

(1+s5)5 = 1+7% =1.07

Thus, s5 = -1 = 1.0136237-1 = 1.3624%

b. Build up the term structure of the forward rates and corresponding zero coupon bond prices

(1+s1)1 = (1+f0,1)1 implies that f0,1 =s1 = 6.00%

(1+s2)2 = (1+s1)1 (1 +f1,1) suggests that 1.0625 = 1.06 (1+f1,1); hence, f1,1 = 0.2358%

(1+s3)3= (1+s2)2 (1+f2,1)

(1+f2,1) = (1+s3)3/(1+s2)2=1.065/1.0625 = 1.002353 meaning that f2,1= 0.2353%

(1+s4)4= (1+s3)3 (1+f3,1)

(1+f3,1) = (1+s4)4/(1+s3)3 = 1.0675/1.065 = 1.002347 simplifies f3,1=0.2347%

(1+s5)5= (1+s4)4 (1+f4,1)

(1+f4,1) = (1+s5)5/(1+s4)4= 1.07/1.0675 = 1.002342 shows that f4,1= 0.2342%

Using excel, the learner proceeds to draw the curve of the forward rates against term to maturity.

Question 2

2×5 swap rate.

Importantly, s3 refers to the 3-year spot rate. Accordingly, (1+s3)3 =1.065 implies that

s3= – 1= 0.021213 =2.121347%

Then, (1+s5)5 = (1+s3)3(1+f3,2)2 simplifies to (1+f3,2)2= (1+s5)5/(1+s3)3 = 1.07/1.065 =1.004695

F3,2 = -1 =1.00234467-1 = 0.2345%

Therefore, the 3-year spot rate is 2.121347% p.a. while the 2-year forward rate is 0.2345% annually.

Term Structure of Forward Rates

Maturity Period (Years)

Forward Rates (%)