Swaps

In CFAI text, on swaps , eg 8 pg 289. Why is the PV of the floating payments = (1+0.045)PV factor? Shouldnt it be automatically 1 as we are on a payment date, as is the case in EOC questions 12 and 13, where the PV of the floating payments on a payment day = 1.

next floating payment = 0.045 is given. in addition it resets to 1… on the payment date

But in EOC questions 12 and 13, we can also find the floating payments and then add it to 1, but in Q 12 and 13, the PV of floating payments =1 (since its a payment date)? So why in eg 8 0.045 was added to 1 (hypothetical notional amt) and not in Q 12 and 13?

this is a special case of marking to market the swap… you are not valuing the swap - here - you are determining what it would take to payoff the existing swap, and entering into a new one… (with the new interest rate schedule) - so that the credit risk gets reduced, or under control.

I do not get the example on Pg289 either . Pg 288 says the present value of floating payments is 1.0 . The very next page says the present value of the floating payments is 1.045(0.9519) =0.9947. I think it should be just 1.0

It goes like this: Because floaters are paid in arrears, the present value at each RESET DATES ONLY is 1. For example, say you have a semi annual pay swap and the the current 180 day libor is 5%. Then your next payment is already know and will be 0.05*180/360. So when you arrive at time 180 days later, you get 0.05*180/360 plus the principal payment 1. Your discount rate is also 5% so when you discount back you get (1 + 0.05*180/360) / ( 1 + 0.05*180/360) which is exactly one. AGAIN, this only happens if you are at a RESET DATE. if you are not at a reset date…say you are 120 days into the contract, so you have 60 days before you get to the next reset date. Now we know that at the reset date, based on the explanation above, the value is exactly 1. BUT we need to discount back 60 more days to today, because we are only 120 days in. So you will discount 1 +0.05*180/360 at a different discount rate (in this case the 60 days libor rate). Hence you will get a different value than 1. Hope this helps

I understand the mechanics , but I think I am missing something. CP: eg 8, EOC questions 12 and 13 are all mark to market, nothing different b/w them. intelo: Your explanation applies to EOC quest 12 and 13, but not to eg 8 on pg 289 where its a reset data and it should be PV =1, but its (1+0.045)PV factor in the eg 8, why this discrpancy?

they gave you in ex 8 that the next floating rate payment is 0.045 (and it is outside of the swap tenure). Orig swap was for 1 year with 180 and 360 day terms. you are on day 360. in the ex. 12 and 13 in EOC - you are at day 180 and day 90 respectively within the swap tenure itself. that seems to be a difference, as far as I can see.

I went through problem 12 in EOC in detail and they work out the case exactly like the example on Pg 288 . I got the same answer too. But the example 8on Pg 289 confuses the heck out of e becos unlike the prob 12 and example Pg 288 , they do not arrive at a value of 1.00 for the floating side even though it is a coupon reset date ( 360 day i.e. second reset ). How come they are different? I checked the errata but no smell there.

the swap in eg 8 is a 2 year swap (not 1 yr), with semi annual payments, and we are in the middle of the tenure (day 360, which is a reset date) and hence PV should be = 1?

actually , cpk , the original tenor was two years with semi-annual payments . Coupon resets are at 180,360,540 and 720 days. We’re now in the 360th day after swap initiation . The original swap is still in effect. A coupon reset means that the floating side owes exactly \$1 , while the fixed side owes \$0.9916 at present discount factors for 180 and 360 days LIBOR. The mark-to-market flow should be 0.0084 per \$1 notional from float to fixed . Instead the example computes as 0.0031 in the same direction. I think they are wrong in the example