value of an interest-rate call option

[raffythebuggy]

Hi! Can someone explain this to me? I do not understand the explanation given in the answer key.
Thanks
The value of an interest-rate call option at expiration is zero or the:
A)
present value of, the market rate minus the exercise rate, adjusted for the period of the rate, times the principal amount.
An interest rate call pays zero or the market rate at expiration minus the exercise rate. Since the payment is made at a date after expiration by the period of the reference rate, the value at expiration is the present value of this difference times the principal value.

 

[villnius]

With an interest rate call option, you have the option to Pay a fixed rate (exercise price) and Rec a variable rate (market rate).
If the option is out of the money (mkt rate is less than exercise rate), it is worthless value is 0. If it is in the money, the value of the option is the differnece in rates (mkt - exercise), times the notional.
Meaning, if you have an option to pay at 5% on 10mm, and mkt rates are 10%, then the value is (10%-5%) x 10mm = 500,000. This makes sense becasue you have to pay 5% on your 10mm notional (500,000), but at the same time can receive 10% in the market (1,000,000). 1,000,000 - 500,000 = 500,000 (value of option)
BUT, since this payment is to be made in the future, it needs to be discounted back to present.