# calcing EAR using interest rate options

this took me a while to really hammer out/understand because i don’t think schweser did a decent job explaining the mechanics of the math in the book. thought it was worth a post: EAR for a firm borrowing from bank using an interest rate call (presumably to protect against rising rates) EAR = ([loan amount + interest received - call payoff] / [loan amount - FV(premium of call)] ^ 365/days of underlying) - 1 basically says that EAR = amount paid to bank / amount borrowed, with the call payoff reducing the amount paid to the bank and the call premium reducing the amount borrowed (since the firm is paying it). makes sense when you really think about the cash flows to the bank i guess. EAR for a bank lending to a firm using an interest rate put (presumably to protect against a drop in rates) EAR = ([loan amount + interest received + call payoff] / [loan amount + FV(premium of call)] ^ 365/days of underlying) - 1 again, basically says that EAR = amount paid to bank / amount lent, with the put payoff increasing the amount paid to the bank and the put premium increasing the amount lent (since the bank is paying it) someone let me know if i’m not thinking about this correctly

Correct me if I am wrong, but here is what I think it should be: EAR for a firm borrowing from bank using an interest rate call (presumably to protect against rising rates) EAR = ([loan amount + interest paid - call payoff] / [loan amount - FV(premium of call)] ^ 365/days of underlying) - 1 EAR for a bank lending to a firm using an interest rate put (presumably to protect against a drop in rates) EAR = ([loan amount + interest received + put payoff] / [loan amount + FV(premium of put)] ^ 365/days of underlying) - 1 The PV of the option premium will be calculated using current libor + basis points (spread)

sorry, that’s right, i copied and pasted the formula without changing the call/put sections