Bank has entered in a long 180-day FRA on the 90-day Treasury rate with the agreed...

Bank has entered in a long 180-day FRA on the 90-day Treasury rate with the agreed upon rate of 2.5 percent. The notional amount is $10.9 million. Calculate the value of the contract 90 days after the start of the FRA if the new forward rate for the same underlying is 2.65 and you know the following spot rates (as of day 90): 90-day: 2.35% 180-day: 2.4% 270-day: 2.55% 360-day: 2.81%

Answer is 4,039.03 not 8thousands. Please provide solution

Expert Solution

Solution:

Given details,
The FRA duration is of 180-days and the underlying is 90-day rate.
Agreed upon rate = 2.5 percent
Notional amount = 10.9 million = 10900000

Current situation,
We are 90 days into this 180-day contract.
New forward rate for the same underlying = 2.65%
And Spot rates (as of day 90): 90-day: 2.35% 180-day: 2.4% 270-day: 2.55% 360-day: 2.81%.
The relevant spot rate will be 180-day spot rate : 2.4% as we have 90 days left in the contract and then the underlying rate is based upon 90-day rate. So, to find the current value we have to discount the final value for the (90+90) 180-days.

Current value of the contract = [Notional Amount * (New forward rate - Agreed upon forward rate)*(90/360)] / [1 + {Existing 180-days spot rate*(180/360)}]
= [10900000 * (0.0265 - 0.0250)*(90/360)] / [1 + {0.024*(180/360)}]
= [10900000 * (0.0265 - 0.0250)*(90/360)] / 1.012
= [10900000 * 0.000375] / 1.012
= 4087.5 / 1.012
= 4039.031621

The value of the contract 90 days after the start of the FRA = 4,039.03

jeff jeffy answered 1 year ago

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