I read that a FRA is equivalent to long a call and short a put…can you explain this? I suppose I get the ‘being long a call’ part- one party has agreed to buy (lock in) the forward rate. But the being short a put part I do not get…
As I understand it:
In a long FRA you receive the floating rate while paying the fixed rate. Let’s say that you pay a fixed rate of 5%:
Assume that at expiration you have a long call and a short put. Let’s think about 2 possible scenarios:
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Interest rates at expiration are 10%: In this case you would exercise the long call option and receive 5%, while the put option would not been exercised by the holder. The premiums received for short put and paid for long call would exactly offset each other.
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Interest rates at expiration are 1%: In this case the put option would be exercised by the holder and you would loose 4%. The long call option however would not be exercised. Again, the premiums offset each other.
Both scenarios replicate to 100% the payments for the long FRA, where you also would receive 5% under scenario 1 and loose 4% under scenario 2.
Regards,
Oscar
It’s no different than saying that owning a stock is equivalent to being long a call option and short a put option, same expiration, same strike.
If you look at put-call parity and solve for the stock price, you’ll see it immediately.