# CFAI Volume 5 Risk Management-Plain Vanilla interest rate swap

Sample question in page 49 of Volume 5 Consider a plain vanilla interest rate swap with two months to go before the next payment. Six months after that, the swap will have its final payment. The swap fixed rate is 7%, and hte upcoming floating payment is 6.9%. All payments are based on 30 days in a month and 360 days in a year. Two-month LIBOR is 7.25%, and eight-month LIBOR 7.375%. The present value factors for two and eight months can be calculated as follow: 1/(1+0.0725*60/360) = 0.9881 1/(1+0.7375*240/360) =0.9531 The next floating payment will be 0.069*180/360 =0.0345. The present value of the floating payments (Plus hypothetical notional principal) is 1.0345*0.9881 =1.0222. Given an annual rate of 7%, the fixed payments will be 0.07 *180/360 = 0.035 The present value of the fixed payments (plus hypothetical notional principal) is, therefore, 0.035*0.9881 + 1.035*0.9531 = 1.021 I am confused by the notional value of fixed payment and floating payment. Why do we need 1? To interest rate swap, the interest income is swapped, not principal . Thanks!

I also don’t see the point of adding 1. But, it doesn’t matter either way. Even if you factor in the principal, it’s the same principal exchanged between the two parties and hence cancel each other out. After all the payments are netted at settlement. So it doesn’t matter what you add to the 2 payments, as long as you add the same amount to both sides.

you solve the value of the swap as the difference between a fixed coupon bond and a floating coupon bond the difference is that, to get current pv, in the case of the “fixed leg” you have to discount every fixed coupon + principa, but in the case of the “floating leg” you have to discount only the next floating payment (which is now fixed according to LIBOR being whatever) plus one (as by definition the floating will be 100% theoretically)