Need help solving and understanding the following 2 part question (A-F): 3. On J
ID: 2774772 • Letter: N
Question
Need help solving and understanding the following 2 part question (A-F):
3. On June 15, 2000 you enter into a 1 –year forward rate agreement (FRA) with a bank for the period starting December 15, 2000 to June , 2001. You know that currently the price of the 6-month zero coupon is $95.75 and the price of the 1-year zero coupon is $92.50. (12.5 points)
A) What is the agreed-upon forward rate in the transaction?
B) What is the value of the forward at inception?
Three months later (September 15) you have second thoughts and you want to get out of the transaction. You receive the data in the following table.
C) What is the value of FRA on September 15, 2000?
Consider now December 15,2000.
D) What is the value of the FRA now?
E) What is the 6-month semi-annual rate?
F) What will the balance to be paid be at the end of the FRA
September 15, 2000 December 15,2000
Maturity Z(0,T) Maturity Z(0,T)
0.25 0.9844 0.25 0.9848
0.50 0.9690 0.50 0.9692
0.75 0.9531 0.75 0.9545
1.00 0.9386 1.00 0.9402
Explanation / Answer
A) Let r1/2 be the 6-month rate and r1 be 1 year rate, 6 month zero coupon price=P1/2 = 100/(1+r1/2*.5)
1 year zero coupon price=P1 = 100/(1+r1*1)
let the Forward rate 6 month from now be r as agreed-upon forward rate in the transaction
=> 1+.5*r =(1+r1*1)/(1+r1/2*.5) = P1/2 /P1 =95.75/92.50= 1.035 =>.5*r=.035 or r=2*.035=.07 or 7%
So agreed-upon forward rate in the transaction is 7%
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