1. Today, ABC Bank (seller) has made a \"three against nine\" FRA, with XYZ Bank

Question

1. Today, ABC Bank (seller) has made a "three against nine" FRA, with XYZ Bank (buyer). Notional amount on the FRA is $10,000,000 and the agreement rate on the FRA is 4.9%. Actual number of days on the contract is 182 days. Suppose, three month later, the market interest rates on LIBOR are quoted as follows. 1-month LIBOR = 4.98% 3-month LIBOR = 5% 6-month LIBOR = 5.03% 9-month LIBOR = 5.0625% 12-month LIBOR = 5.08% (1) Calculate the cash settlement of the FRA transaction (2) Who receives the cash settlement? ABC Bank or XYZ Bank?

Explanation / Answer

Answer (1)

Cash Settlement amount = $ 6409.24

Answer (2)

The amount is to be paid by ABC Bank to XYZ Bank

Notional Value of FRA = $ 10,000,000

Agreement rate on FRA = 4.9%

Actual Number of days in contract = 182

Reference rate or Floating rate to be taken on 3 against 9 basis = Termination date of contract 9 months – Effective date of contract 3 months = 9-3 = 6 Month LIBOR

Given 6 month LIBOR = 5.03%

Payment can be calculated using the below formula

Payment = Notional Amount * [((Reference rate – Fixed rate) *(Number of Days/360)) / (1+reference rate * (Number of days/360))]

Payment = $ 10,000,000 * [(0.0503 – 0.049)*(182/360))/(1+(0.0503 * (182/360))]

                  = $ 10,000,000 * [(0.0013 * (182/360) / (1+ 0.025429444)]

                  = $ 10,000,000 * [0.0006572222/1.025429444]

                  = $ 10,000,000 * 0.0006409238842

                  = $ 6409.238842 or $ 6409.24 (rounded off)

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