Fixed Payer vs. Receiver Swap Rates

CFA Level II Derivatives
#1

Hello,

Swap rates are one of the difficult topics for me and still cannot get my head around it…

There is one question that gives you a set of LIBOR rates (semi-annual coupon rates for two years)

180 Day - 5%

360 Day - 6%

540 Day - 6.5%

720 Day - 7%

Swap rate is something like 0.0331 (unannualized). Gets multiplied by two because this is a semi-annual rate, so I get that.

Now, moving 180 days forward, new LIBOR rates are:

180 Day - 4.5%

360 Day - 5%

540 Day - 6%

With the respective discount rates, I apply them to the unannualized swap rate (original as calculated above) and add $1 * discount factor that is the latest (in this case, 540-day rate). So the answer becomes that fixed-payer marks the swap to market by paying $0.01166.

My questions are:

#1 When rates changed, does that mean the swap rate has gone down because the lower LIBOR rates? I’m having difficult times understanding the new LIBOR rates in relation to the old set of rates.

#2 If the above is true (or false), why do the discount factors go the opposite way (discount factors are higher implying rates have gone up)

#3 So assuming the #1 is correct, are we saying the fixed-payer has to mark to market because, since the swap rate has gone down compared to the original, fixed-payer receives less on their float side, therefore that forces them to mark to market?

Thank you in advance.

#2

1.) When rates change, the original swap rate does not change. However, you could go into a new swap at a better or worse rate. So to value your current swap you find the new swap rate and then do some math versus your old swap rate. Or you can take discount factors with your current cash flow based on the new rates to find the value

2.) Discount factor is inversely related to the rate. Rate goes up, discount factor goes down.