# Swap - Floating Payments

Example: Pay fix and receive floating with two settlements remaining; the next in 30 days and the last in 120 days. LIBOR was 3.04% at the last settlement date and the swap fixed rate is 3%. 30-day and 120-day LIBOR are 3.05% and 3.10% respectively. Calculate the amount of credit risk. PV of swap Fixed Payments: [(\$0.0075) / (1.0305) 30/360] + [(\$1.0075) / (1.0305)120/360] = \$1.0047 PV of swap Floating Payments: [(\$1.0076) / (1.0305) 30/360] My question is on the calculation of Floating Payments. what is the logic (in plain English) behind why we are discounting the sum of principal and interest only once with the rate of 30-day LIBOR. I need to understand the logic behind this. Please help.

floating coupon resets to par.

ok, and that is the explanation in the book but when you receive float, don’t you receive pv of settlement periods (the same way you are paying to fix) plus pv of NP? this is where I am really confused. why would you calculate pv of all the settlements and pv of NP in the calculation of Fixed payble but not in the Float receivable? I skipped swaps completely at both previous levels so my question may be very basic to you guys.

because the float resets to par, you know it will be at par at the next reset (in this example, it would be 30 days). Since it automatically resets to par, your only interest payment is the one that is coming up. So for float, you always have to worry about the NEXT payment (sorry for the caps, i can’t italicize). Fixed is only giving you interest each payment period until the last payment were you would receive the principal. Thats why you have two different discounting calculations for the fixed payment in your example. If you notice, you will see the final payment has the “1” in it since it is returning principal. hope that helps

deep2002 Wrote: ------------------------------------------------------- > because the float resets to par, you know it will > be at par at the next reset (in this example, it > would be 30 days). Since it automatically resets > to par, your only interest payment is the one that > is coming up. So for float, you always have to > worry about the NEXT payment (sorry for the caps, > i can’t italicize). > > Fixed is only giving you interest each payment > period until the last payment were you would > receive the principal. Thats why you have two > different discounting calculations for the fixed > payment in your example. If you notice, you will > see the final payment has the “1” in it since it > is returning principal. > > hope that helps Thanks! I understand the calculations and logic behind the Fixed. It’s the Float that throws me off. So, in swap, Fix pays interests at each period plus principal at the end, but Float pays only one interest payment plus the principal payment at the end?

Hi Ashwin, For the fixed payments, in the calculations that you have shown: PV of swap Fixed Payments: [(\$0.0075) / (1.0305) 30/360] + [(\$1.0075) / (1.0305)120/360] = \$1.0047 For the principle repayment part, don’t you mean 1.310 and not 1.305? According to your problem - “30-day and 120-day LIBOR are 3.05% and 3.10% respectively”. Pls. confirm this. Thanks

might help if you dragged out your books from Level II and read up. otherwise - search Level II Forum for a post by JScott (On Swaps and FRAs, 2 separate posts). They would help you a lot. Float would receive Principal which is the 1 Part. The 0.0076 - Last period was 0.0304 quarterly. That is 0.0076. So total payment is 1.0076, and you are receiving it at the 30 day mark, where LIBOR is 3.05%. So you get 1/(1+0.0305*30/360) * 1.0076. You also have the factor written down wrongly as 1.0305*30/360 -> it should instead be 1/[1+ (0.0305 * 30/360)] --> bracketing shown is important. It is a value of 0.9974 for your reference.

sparty419 Wrote: ------------------------------------------------------- > Hi Ashwin, > > For the fixed payments, in the calculations that > you have shown: > > PV of swap Fixed Payments: [(\$0.0075) / (1.0305) > 30/360] + [(\$1.0075) / (1.0305)120/360] = \$1.0047 > > For the principle repayment part, don’t you mean > 1.310 and not 1.305? According to your problem - > “30-day and 120-day LIBOR are 3.05% and 3.10% > respectively”. > > Pls. confirm this. > > Thanks yes, you are correct. It should be discounted by 3.10%.