Question

Trade setting, January 16, 2020 Suppose that a bank trading desk has just entered into a hypothetical 2x5 “squared" FRA where the bank pays a fixed rate and receives LIBOR x LIBOR in return. For example, if LIBOR=5%, the bank would receive 25% against the fixed rate. Suppose the timing of the cash flows in this 2x5 “squared" FRA is similar to those in a plain vanilla 2x5 FRA. 3-month LIBOR is set on March 16 and the FRA is cash settled (i.e. payment is made) 2 business days later (March 18) based on the actual number of days in the 3-month period beginning March 18. The FRA differs from the standard 2x5 only in that the bank receives the value of LIBOR x LIBOR rather than just LIBOR. Assume that the fixed rate the bank pays is 30% and the transaction is based on a notional amount of $100 million. Also, assume that 2 month LIBOR on January 16 equals 5.3%. 1. What is the payment the bank trading desk will make or receive on this transaction on March 18, if 3-month LIBOR equals 5.3 percent? Where do you think the forward 2x5 rate is assuming that the trade has just been completed and that no cash was exchanged up front? Hint: the forward rate should be the one that makes the NPV of the transaction equal to zero. 2.

Answer 1

Part (1)

Convention will be actual / 360

Actual nos. of days in 3 months starting Mar 18 = 31 + 30 + 31 = 92

Payment trading desk will make = Notional principal x fixed rate x actual number of days in three months period / 360 = $ 100 million x 30% x 92 / 360 = $ 7.56 million

LIBOR = 5.3%

Floating rate = LIBOR x LIBOR = (5.3 x 5.3) = 28.09%

Payment trading desk will receive = Notional principal x floating rate x actual number of days in three months period / 365 = $ 100 million x 28.09% x 92 / 360 = $ 7.08 million

Hence, the payment trading desk will receive a net amount of 7.56 - 7.08 = $ 0.48 million = $ 481,425

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