# Swaps

Vol5- SS13- Reading 38- Pg154- Q.4 I don’t quite follow the solution. so if in 1 year, we are overpaying by .952, how does it increase to 1.01866? from where do we get the figure of 1.070024? and then how the total accumulative payment becomes .97066 in year 2…the interest payment thing is a bit confusing.can anyone help?

you just carry forward the over/under-payments at each settlement date by the implied forward interest rates using the spot rates given. After you carry the 0.952 overpayment forward, net it out with the 2nd year’s over/under payment, then carry that number forward by the next forward interest rate. In the end the over/under payment should net to zero. Sorry for the lack of specificity, i’m working from memory.

thanks for replying but i’m afraid i still don’t follow. i mean i get it that u have to net it out with the 2nd yr’s over/under payment but i don’t understand how they calculate the implied forward interest rates in the solution. anyone?

the overpayment of 0.952 in the first year, is sorta like a loan to the other party. That increases by 1.070024. This implied interest rate is calculated by using bootstrapping with the 1-year and 2-year forward rates (don’t have the books in front of me…but that’s what i vaguely remember…) = (1.065 ^2)/1.06 = 1.070024. so in effect, this overpayment (which is a loan from the other party’s perpective grows over one year by the implied interest rate of 7.0024. similarly the overpayment for the second year is another short loan …interest is calculated similarly. the final payment if i remember is underpayment - which is equal to the sum of the two overpayments (including the interest)…so in total the value is zero…

Just notice also that there’s a big section of the reading 38, which are optional. Any chance of having questions on that section for the exam?

No. Not if it is marked as optional. It may help you understand other sections though.