Value to payer - Derivatives

Hi, could anyone explain the logic behind the below question? Is there a reason why I can’t get the answer thru the regular approach of two bonds?

A $10 million 2-year semi-annual-pay LIBOR-based interest-rate swap was initiated 180 days ago when swap fixed rate was 3.8%. The fixed rate on the swap is now 3.4% and the term structure is as follows:

Days LIBOR Discount Factor 180 3.00% 0.98522 360 3.20% 0.96899 540 3.40% 0.95148 720 4.00% 0.92593

Value of the swap to the payer is closest to:


Sum of the discount factors for the three settlement dates remaining (180,360 and 540 days away) = 0.98522 + 0.96899 + 0.95148 = 2.9057

Value to payer = 2.9057 x [(0.034 - 0.038)/2] x $ 10 million = -$58,114

S2000 - Heed our call, for we require your guidance on this troubling day.

tough, i do not recall learning how to value swap when the fix rate change. where do you get this question from?

Schweser qbank

I don’t remember that short formula off the top of my head, but the way I understand it is the value to the long party at any time during the life of the swap = the present value of the difference in remaining payments if they were to enter into another swap today as the short (pay variable, receive fixed) given the current term structure of LIBOR.

E.g., 180 days ago you agreed to pay 3.8% semi-annually (or $190,000) for variable payments for 2 years. Today, 0.5 years later, the swap fixed rate stands at 3.4% given LIBOR term structure. So if you entered into the offsetting position today to receive fixed, pay variable, you’d receive only $170,000 semi-annually until the swap expires. The difference between these two are -$20,000, with 3 remaining payments. The present value of each of those -$20,000 in 180, 360, and 540 days from now (the remaining payments in the swap’s life) = -$58,113.8. I think I recall a similar problem (see above) What this seems to suggest is that you had initially locked in a 3.8% swap rate (annualized). Based on the latest interest rates, the new equilibrium swap rate is 3.4% (lower than what you locked in a year earlier). The variable payments received are the same in both cases , so you don’t need to worry about it. The value to the pay is thus the amount they’re paying more by locking in a higher fixed rate swap from a year earlier. The fixed semi-annual coupon payments were 3.8%/2 = .019. The PV per NP is .019 \* .98522 + .019 \* .96899 + 1.019\* .95148 = 1.00669 (adding 1 to the last payment because they're getting the principal back). The fixed semi-annual coupon payments on a swap now is 3.4%/2=.017. The PV per NP now is the same as above, but replace .019 with .017. The PV is 1.00088. The value to the payer is how much less he is paying = (PVold - PVnew) * NP

Thanks, this makes much more sense.

Do you think it would have been difficult for them to word that as “what would be the value against the offsetting position?” The way I read it originally it seemed like the second swap rate was a red Harring because ultimately the value to the payer is dependent on the original swap cash flows. I could easily see my self on exam day addressing this question looking to value the swap that was entered into with the libor rates 90 days later. Any insight to how you identified what exactly they are asking for prior to the answer?

when i take a look again at this question, it asks for the value to the fixed rate payer, not the total swap value. thus, we do not need to calculate the floating leg

Agreed the question says value to the payer, however value to the payer in absolute terms is also the value to the receiver, no? When they ask value to the payer it just becomes a question of if they are losing value Ig or gaining it in my mind. When I value this swap as a floating rate note and fixed rate note my value is different than the answer because I didn’t look at it as an offsetting position.

I am still not sure why I would look at an offsetting position for a fixed rate that I don’t have a contract for. The value of the swap in this case is based on the rate at inception. If the question were “what is the difference in value between the two” or something along the lines of “how much has the payer lost in relation to what contracts are going for today” would make more sense to me. Not trying to be picky, just trying to be certain I read these questions in the way everyone else seems to see this as. If you have any insight to what lead you in the direction of an offsetting position as opposed to valuing the swap it would be greatly appreciated.

The value to the long party is the value to the short party, except one of theirs will be positive and the other negative. In your earlier example, the value to the long party = -$58,114, the value to the short party = +$58,114.

The offsetting position is simply the trade you’d need to place in order to “get out” of your position. If you’ve contractually agreed to receive floating LIBOR and pay 3.8% fixed for the next few years and wanted to offset (“get out”) the position today, you’d need to sell this swap (which is in effect entering into a contract today of the same maturity) to pay floating LIBOR and receive fixed. If the fixed rates are different from the fixed rate you agreed to pay when you put on your first long position, your value will be different from zero.

I follow you on all of that. My concern lies in what they asked for and me not recognizing it as that.

They ask what is the value of the swap. I calculated that as 1-1.00669=-.00669. So the value of the swap is -66,900.

I get the approach with an offsetting position to liquidate with current fixed rates.

I am completely lost on how everyone made the distinction that we were liquidating instead of valuing the swap. What gave this away that they were asking to value against an offsetting position and that they didn’t just give you the second swap fixed rate to mislead you? The question only asked what is the value of the swap.

Hmm, odd wording then. I think this is more semantics than anything else.