 # Schweser swap question

On page 300 of the FI and derivatives book, question 9 reading 65. I read the explanation and I don’t understand it. If someone here understands it could you explain how you do it? There is a 2 year plain vanilla swap with semiannual payments with an annual swap rate of 6.62%. After 180 days the swap is marked to market when the 180, 360, and 540 day annualized LIBOR rates are 4.5%, 5%, and 6% respectively. The present value factors, respectively are .978, .9524, and .9174. What is the market value of the swap per 1 of notional principal and which of the 2 counter parties (fixed rate payer or fixed rate receiver) would make the payment to mark the swap to market? Market Value Payment made by A. .01166 Fixed rate payer B. .04290 Fixed rate payer C. .01166 Fixed rate receiver D. \$.04290 Fixed rate receiver

Value of floating = (1 + .045 / 2) * .978 = 1.00001 Value of fixed = .0331(.978 + .9524 + .9174) + .9174 = 1.01166 Payment made by fixed to floating = .01165 = So A? Things to note is that for the floating you consider only the next payment because the value of the floating on the settlement date is 1 (including the hypothetical notional principal). For floating you are value it like a coupon bond with coupon = fixed rate and coupon payments at 180,360 and 240 with return of hypothetical notional principal of 1 at the end of the swap.

dumb question- do you use the 4.5% here or the original 6.62% for the 1st floating guy payment? Either way I get A as the answer- if 4.5 then exactly what SV said… if it were the original 6.62% just replace the 0.045 on top by 0.0662 to get floating at 1.01037818… either way fixed is the loser on the 1st one so I’m with A. fixed above looks good to me.

A value of fixed receiver > value of floating receiver so fixed rate PAYER pays to receiver value of fixed: 6.62% /2 = 3.31 payments 3 more payments left multiply each one by the PV factor (given) but add 1 to the last one for principal PVs: .0324 + .0315 + .9478 = 1.01166 Value to floating: equal to 1 on payment dates since floating rate resets so, fixed value is > by .01166

^ bam there’s my answer. it’s on reset day so it’s = 1. THANK YOU.

yeah sv’s way works too but if its on reset always remember the floating rate bond is 1… saves 45 seconds of work! here is something i could see them asking… waht is the duration of the floating rate leg on reset? its equal to the term of the reset… so semiannual swap would be a .5 duration, quarterly .25, etc. only sensitive until it resets

Why can’t Schweser explain it as well as you guys?

Actually the way i understood it is just before the reset? Basically they want the value at expiration? After the reset it is 1, but before the reset you need to consider the floating payment. If it was after the reset, we would not consider the payment for the 180 day righ? Am i missing anything here?

I go with A as well…

sv - i think if it says at a payment date - you assumed it’s been reset and hence the value is = 1

–>Value of floating = (1 + .045 / 2) * .978 = 1.00001 -->Value of fixed = .0331(.978 + .9524 + .9174) + .9174 = 1.01166 Can anyone explain this calculation? Specifically, what’s the rationale for 0.331(.978 + .9524 + .9174) Thanks,

I did this problem similarly to sv. new price of the swap = 5.8% = (1-.9174)/(.978 + .9524 + .9174) X 2 Value to Fl Rec. = (.0662 - .058)/2 = .0041 .0041(.978 + .9524 + .9174) = .0116

0.331(.978 + .9524 + .9174) This is just discounting the fixed payments back to today.

^^mumu question says what payment would mark the swap to market. So before reset. right?

yeah…but in that case you wouldn’t use 4.5% - that’s the new LIBOR at day 180 for the next payment… If it’s just before reset you would want to discount the payment on day 180 which would actually be decided based on what the 180 LIBOR was when the contract was initiated - and the discount factor would be what…just a millisecond? if it’s just before reset… doesn’t make sense…you see what I’m getting at??

phBOOM Wrote: ------------------------------------------------------- > -->Value of floating = (1 + .045 / 2) * .978 = > 1.00001 > -->Value of fixed = .0331(.978 + .9524 + .9174) + > .9174 = 1.01166 > > Can anyone explain this calculation? Specifically, > what’s the rationale for > > 0.331(.978 + .9524 + .9174) > > Thanks, Since its a semiannual swap you take the annual swap rate % 2. You multiply it by the sum of the discount factors to bring it back to present value. The floating rate payment is the semiannual coupon rate before payment discounted back, plus the 1, because the floating rate always resets to par.

Got it mumu. I had a light bulb moment during dinner 