# payoff timing of FRA & Interest rate option

Maybe it would be really basic concept but I am still a bit confused. 1. In FRA, the payoff timing is the end date of the underlying loan. So when we value the FRA, we present value the payoff amount once to the date loan starting & one more present value the amont to the date we are on. 2. But In interest rate option I would like to know when I should think of the payoff date is. The underlying loan starting date ? or loan end date? I thought it was loan starting date different from the FRA but it seems that there was a recent question in that it was the same as the FRA, the end date of the loan. For example, \$ 100, 5% strike rate. Now year 1999 Jan. Loan start 2001 Jan. Loan ends 2001 Dec 31. In 2000 Jan the forward rate for 2001 became 6%. what is the value now on 2000 Jan 1st? 1st answer, the payoff is \$1 at 2001 Dec 31 the PV of it on 2001 Jan \$1 * 0.9 (present value factor - assumption) = 0.9 the value of it on 2000 Jan (now) = 0.9 * 0.91(present value factor) = 0.819 2nd answer, the payoff is \$1 at 2001 Jan the value of it on 2000 Jan (now) = 1 * 0.91 = 0.91 which answer is right?

Interest rate option should be settled in arrears based on rate at time of reset and days in the period. It is common place to PV the payment for the period as it is known with certainty before beginning. 1st answer is correct IMO.