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Question on FRA

A bank sells “three against nine” $3,000,000 FRA for a six-month period beginning from three months from today and ending nine months from today.  The reason of the FRA is to cover the interest rate risk caused by the maturity mismatch from having made a three-month Eurodollar loan & having accepted a nine-month Eurodollar deposit.  The agreement rate along the buyer is 5.5 percent.  There are in fact 183 days in the six-month period.  Suppose that three months from today the settlement rate is 4 7/8 percent.  Estimate how much the FRA is worth and who pays whom the buyer pays the seller or the seller pays the buyer.

As the settlement rate is less than the agreement rate, the buyer pays the seller the absolute value of the FRA.  The absolute value of the FRA is following:

 $3,000,000 x [(.04875-.055) x 183/360]/[1 + (.04875 x 183/360)]

      =  $3,000,000 x [-.003177/(1.024781)]

      =  $9,300.52.

 

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