Interest rate options

R33. Ex11. Q01.

In this question the options is in the money and exercised, but the effective rate on loan (9.25) still ends up being higher than libor (6+3).

What makes it okay to exercise the option then? the combined cost of not exercising + option premium would make it steeper?

Because it’s an annualized rate. If the payoff of the option was zero, the annual rate would be: ($5,112,500/$4,989,912)^(365/90) = 10.34%.

9.25% < 10.34%