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Question 5.A bank has borrowing needs at timeT >0. Show that by combining an FRAtrade today with a libor loan at timeT, the bank can today lock in its interest cost forthe periodTtoT+α. Does the borrowing bank need to buy or sell the FRA to do this?What is the fixed rate that the bank locks in?

Question

Question 5.A bank has borrowing needs at timeT >0. Show that by combining an FRAtrade today with a libor loan at timeT, the bank can today lock in its interest cost forthe periodTtoT+α. Does the borrowing bank need to buy or sell the FRA to do this?What is the fixed rate that the bank locks in?

check_circleAnswer
Step 1

An agreement which states that lender (seller) will lend a fixed sum of money to borrower (buyer) at predetermined rate of interest on fixed future date and for specified term is known as forward rate agreement. Under forward rate agreement, seller has the option of cash settlement on exercise date.

Step 2

Assumptions:

Number of shares purchased by the bank today is N.

Bank will receive a LIBOR loan at future date T and pay on T+α.

According to above assumptions, Bank will have a cash inflow of N dollars at T. Further, bank also has a cash inflow of (LT [T, T+α]-K) according to forward rate agreement.

Bank will have a cash outflow of N(1+αLT [T, T+α]) to pay off the LIBOR loan.

Step 3

The total amount paid by the bank at tim...

N1+aLr[TT+a]-Na{L, [T,T+a]-K )=N+NaL,[T,T+a]-Na,[T,T+a]+NaK_
-N+ΝαΚ
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N1+aLr[TT+a]-Na{L, [T,T+a]-K )=N+NaL,[T,T+a]-Na,[T,T+a]+NaK_ -N+ΝαΚ

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