# What is equivalent to a long FRA?

Suppose a forward rate agreement (FRA) calls for the exchange of six-month London Interbank Offered Rate (LIBOR) two years from now for a payment of a fixed rate of interest of 6%. Which of the following structures is equivalent to this long FRA? A long:

A) put and a short call on LIBOR with a strike rate of 6% and two years to expiration. B) call on LIBOR with a strike rate of 6% and eighteen months to expiration. C) call and a short put on LIBOR with a strike rate of 6% and two years to expiration.

Assume at the end of year 2, 6-month LIBOR = 7% … what happens then?

Assume at the end of year 2, 6-month LIBOR = 5% … what happens then?

I would say B - call on LIBOR with a strike rate of 6% and eighteen months to expiration.

Is that correct?

As Per my understanding, I would say the answer is C) call and a short put on LIBOR with a strike rate of 6% and two years to expiration.

In a FRA, you pay Fixed and Receive Floating. A Long call and short put with a strike rate of 6% would replication that while offseting the option premium paid for the long opion with the premium received for the short opens.

2 Years later, If the Interest rates are at 7%, you would exercise the call option and pay 6% and recieve 7%, while the put option would go unexercised.

If the Tares fall to 5%, then you wouldnt exercise the call option, with the put option being exercise by the holder, where you would pay 6% and receive 5%.

This is how I see it. I am quite weak in Derivative, so it would be great if somebody could validate my answer.

Well done. I couldn’t think through this clearly. You got it… I give you A+.

1. After two years if int% is 7%:

Without the options, you pay fixed 6% and receive 7%, you’re up +1%.

With long call, short put: you get +1% from the call, and the put is worthless for the holder, you’re up +1%.

1. After two years if int% is 5%:

Without the options, you pay fixed 6% and receive 5%, you’re down -1%.

With long call, short put: the call you own is worthless, but the put holder will have you pay him/her 1% (6% strike - 5% rate), you’re down -1%.

* The only difference I see is if the cost of the call is not fully offset by the premium you collect from the put, then, you are not replicating the swap 100%.