Question

You enter into a forward contract to buy a 10-year, zero coupon bond that will be issued in one year. The face value of the bond is $1,000, and the 1-year and 11-year spot interest rates are 5 percent and 7 percent, respectively.

What is the forward price of your contract?

Suppose both the 1-year and 11-year spot rates unexpectedly shift downward by 2 percent. What is the new price of the forward contract?

Answer 1

Solution :

1 year spot rate = S1= 5%, 11 year spot rate =S11= 7% ,

We have to find the forward rate for 10 year and it starts after one year

So ,

(1 + S1)^1 * ( 1+ 1F10)^10 = (1+S11)^11

(1+0.05)^1 * ( 1+ F )^10 = (1+0.07)^11

(1+ F)^10 = 1.07^11 / 1.05 = 2.104852/1.05 = 2.004621

1+ F= 2.004621 ^(1/10) = 1.072021

F = 1.072021 - 1 = 0.072021 = 7.2021%

Forward price of the bond = face value / ( 1+ 0.072021)^10 = 1000/1.072021^10 = 498.84

If interest rate change by 2 % then 1-year spot rate = 3%, 11 year spot rate = 5%

Using the previous formula

(1+ F)^10 = 1.05^11 / 1.03 = 1.710339/1.03 = 1.660524

1+ F= 1.660524 ^(1/10) = 1.052021

F = 1.052021 - 1 = 0.052021 = 5.2021%

Forward price of the bond = face value / ( 1+ 0.052021)^10 = 1000/1.052021^10 = 602.22