# Options derivs- highest possible EAR

I don’t get the concept of “highest possible rate” for the EAR when calculating ir options. For example when you are calculating this for a long call IR option with strike 4.5% schweser says that the EAR that you get won’t get higher with values of Libor above 4.5%. Confused does someone understand this please? Thanks!

Let’s say that LIBOR was initially 3% and suddenly goes up to 18% p.a. and your loan happens to be a LIBOR floating rate loan (reset annually). You now have to pay an additional 15% of interest expense, i.e. earnings drop by 15% × Loan amount (for the next one year).

With the IR call option, the payoff will be:

Max(0,18%-4.5%) = 13.5%

When you combine the loan interest and the call payoff you only pay 18% - 13.5% = 4.5%

In other words, the IR call option payoff will always offset the overall interest expense to 4.5% when the LIBOR goes above 4.5%.

If the LIBOR goes below 4.5% then you benefit from paying less interest (assuming you have more interest rate sensitive liabilities than assets)