Question

a)Find the spot rates implied by the prices of the bonds below each of which are F = C = 1000 with 10% annual coupons. Each makes coupon payments once per year. Bond Term Price 1 1 year 1028 2 2 years 1035 b) What is the value of the forward rate 11.2?

Answer 1

Current price of a bond = Present value of all the coupon payments + Present value of face value

R1 is spot rate for one year

R2 is spot rate for two year

i1,2 is forward rate

Coupon amount = (10/100)*1000= 100

a)

Bond1:

1028 = 100/(1+ R1) + 1000/(1 + R1)

R1 = 1100/1028 -1 = 0.0700389 = 7.00389% (spot rate for one year)

Bond2:

There would be two coupon payments for this bond, one would be paid at the end of the first year and another would be paid at the end of the second of the year.

1035 = 100/ (1+r1) + 100/(1+R2)^2 +1000/(1+ R2)^2

(1+ R2)^2 = 1100/941.5454

R2 = 0.08087 =8.0875 % (spot rate for two year)

b)

(1 + i1,2) = ( 1+ R2)^2 / (1+R1) = 1.091821

i1,2 = 9.1821% Answer