# Payoff Date of Interest Rate Options

I don’t know why I still have questions on Options. Here is another: When we calculate the effective [borrowing] rate for a borrower(loan+call), why is the Payoff of the interest rate Call option received at the end of the loan(instead of the expiration date of the Call option itself)?

Great question. I wondered the same thing. In fact, if you look a few pages before when the loan+FRA is calculated, the payoff is discounted to PV.

deriv108 Wrote: ------------------------------------------------------- > I don’t know why I still have questions on > Options. > > Here is another: > > When we calculate the effective rate for a > borrower(loan+call), why is the Payoff of the > interest rate Call option received at the end of > the loan(instead of the expiration date of the > Call option itself)? Isn’t it because you enter into a contract giving the right, but not the obligation, to buy or sell a financial instrument paying a fixed rate of interest at a specified price and future date. In December you enter into a contract that you might buy a financial instrument in February whose interest you will pay in April. You can enter that contract in Feb too but the interest rates might not be in your favor.

it would be wrong to calculate the pay off on expiration of the call because even though the interest fixed at the expiration date, the interest is PAID in arrear long in the future (i.e., when the loan in finally paid off), thus you need to discount that gain/loss back. Interest rate option is the option to get a fixed rate while FRA is an obligation to get a fixed rate thus the payoff of the option is quite similar to pay off FRA calculation at expiration.

The payoff is not in cash form , it is in the form of a reduced loan rate( can’t take that to the bank) To convert the reduced loan rate to its present value you must discount the amount of the loan at the call strike rate over the term of the loan

The CFAI doesn’t discount the option payoff to PV but it discouts the FRA payoff to PV.