Based on http://www.xavier.edu/williams/centers/trading-center/documents/research/edu_ppts/03_InterestRateSwaps.ppt (downloaded to C:\0x\88_xz_ref)

On P54 the “closing a swap position” discussion is … very relevant. Start at the example on P57.

On T+0, enter 5.5%/Libor swap as fixed payer.

On T+1Y, prevailing (par) swap rate drops to 5%. Bad for the fixed payer as she has commitment to pay 5.5%. She wants out, and she doesn’t need any more loan. You can assume she has cancelled her project altogether. So she would hedge out her floating exposure and realize any loss on the fixed leg.

Specifically, she enters a new swap as a fixed Receiver this time, receiving (the lower) 5%. The new floating leg perfectly cancels the existing floating leg, with identical payment dates.

As a result, for the next 4 semi-annual payments, she would receive 2.5% and pay 2.75% every time. This is the kind of loss she must accept when closing the swap in an unfavorable market. If you sum up the present value of these 4 negative cashflows, you see the (negative) present MV of the fixed position. (Note each swap deal has a $0 market value at inception.)

(The “fixed position” means the position of the fixed Payer.)

As of T+1Y, the fixed position has a negative mark-to-market value given on P60, -$94,049 on a $10m notional.

It follows that to the original fixed Receiver, this existing swap deal now has a positive market value. Intuitively, this receiver is paying a below-market rate (5%/year) to receive the stream of floating coupons (i.e. the silver). The same stream is currently selling at 5.5%.

Yes it’s confusing! I feel the keys are

1) how to cancel out the floating leg exposure. You will then figure out that to close the swap, you need to take up a new fixed leg.

2) That would tell you the upcoming cashflows are positive or negative.

3) By summing up the PV of those cash flows you get the current MV.

Final MV formula is on P70.