# can someone pls explain this to me?

Suppose a forward rate agreement (FRA) calls for the exchange of six-month LIBOR one year from now for a payment of a fixed rate of interest of 8 percent. In other words, pay floating and receive fixed. Which of the following structures is equivalent to this FRA? A long: A) call on LIBOR with a strike rate of 8% and six months to expiration. B) call and a short put on LIBOR with a strike rate of 8% and six months to expiration. C) put and a short call on LIBOR with a strike rate of 8% and twelve months to expiration. D) call and a short put on LIBOR with a strike rate of 8% and twelve months to expiration.

B?

D?

B makes the most sense to me, but not that much sense.

I’d also go with b, but my logic could be wrong. can’t you eliminate c or d because the exchange of money happens in a year? if money gets exchanged in a year, the actual agreement for six month libor has to kick in 6 months from now, no?

h= 1 yr m= 0.5 yrs. 6 month LIBOR rate is the LIBOR rate on which the FRA is based. But the agreement itself comes to an end after 1 yr. That’s what I think. Correct me if I’m wrong.

Hopefully I figure this out when I start derivatives tomorrow. Looking at it again from the point of the fixed receiver. If you are locked into receiving fixed, you gain when the floating rate is below the strike rate because you are receiving a higher payment than you can currently get on the market. Gain when rates decrease = long put You lose if rates go above the strike rate because you are locked in at 8% when you could get higher than that on the market. Lose when rates increase = short call. So C?

^^ Makes sense too. I worked it out numerically. Suppose the rate is 9%. You receive the fixed rate of 8% and pay the floating rate 9%. Netted= pay 1%. Now, if we go Long call and short put with 9% in mind=== Long call is worth 1%, which you will be paying, because you are long. The put expires worthless. Again, if the rate is suppose 7%. You receive 8% fixed and pay 7% floating. Net gain= +1% Long Call here with a strike rate of 8% would expire worthless. Short Put means -(7-8)=+1%. So, D in confirmation with the original statement.

It should be C. Paying float means that if interest goes up, you lose which is equivalent to interest rate put.

when interest rate increase, it will benefit- same as long call payoff when interest rate decrease, loss- same as short put payoff its D.

b, what does schweser have to say about it?

It has to be C…the time has to match up. If it calls for the exchange one year from now, then the option needs to expire 1 year from now. If you pay floating and receive fixed, you benefit when rates go down. If you write calls, your benefit from rates going down, and gain when rates go up b.c as rates go down, you get the premium for wtring the call but the underlying wont get snatched from you cause it is less likely to move above strike price. If rates fall, and you are long puts, you benefit

If you pay want to replicate a pay floating and receive fixed, I would think you would need to long a call and short a put.

Dand C are the same thing from a different perspective. This says “pay floating and receive fixed” so presuambly that’s the perspective you want to take. That means you want interest rates to go down (try interest rates go to 0 and see how much you like that). Which means you want LIBOR to go down which means you want a long put and short call on LIBOR. which would be…C

Edit: ignore me

C

looks like its C then

Sweet . . . . to bad I got it wrong on my first try.

i was thinking C… and after choosing that, was concerned there were no C guesses at the top of the thread… lots further down… you get hurt if libor goes way up, therefore short call… you benefit if libor goes way down, therefore long put… don’t really know this section that well though 12 month contract as then the libor will be for the next 6 months…

I want to start thinking in this direction: If I *buy* LIBOR, I’m receiving LIBOR rates. Since I’m paying float, I am effectively selling LIBOR, thus the short the call on LIBOR. But what about long the put? I can’t seem to get my arm around this one.