## Interest Rate Options Explained

Unlike Forwards and Futures, Options give the holder the right but not the obligation to buy or sell the underlying asset at a future date negotiated on a fixed price. As known, they are call and put options.

An interest rate call is an option in which the holder has the right to make a known interest payment and receive an unknown interest payment. So underlying asset is unknown interest rate. You can think of that as buying a LIBOR rate. If the LIBOR rate is higher than the exercise rate at expiration, the option is in the money and is exercised, otherwise you just leave it.

An interest put option gives you the right to (sell) make an unknown interest payment and receive a known interest payment. At the end of contract period, if the unknown underlying rate is lower than the exercise rate at expiration, the option is in the money.

For example consider a 3×9 Forward Rate Agreement call option which means 180 day LIBOR expiring in 90 days. The option buyer specifies an exercise rate of 5.5 % and notional principal amount is $10 million.

At the expiration day if the interest rate is 6% that means call option holder will have the right to receive the unknown interest rate which was 180 LIBOR at expiration (6%) and pay the rate they have fixed at the beginning of agreement (the exercise price) , 5.5% . Obviously, this option is in the money. Pay off to holder of the option is

$10,000,000 (0.06 – 0.055) (180/360) = $25,000

But that means this $25K is the amount you will receive if you invest on 180 days LIBOR. So you have to bring this money back to today’s value which is simply the Present Value of $25K @ 6%

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