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### Subject 10. Netting and marking to market

Netting reduces the credit risk in a swap by reducing the amount of money passing from any one party to another. The amount owed by a party is deducted from the amount due to a party, and only the net is paid.

Marking a swap to market is a process in which the parties agree to periodically calculate the market value of the swap and have the party owing the greater amount pay the market value to the other party. The fixed rate is then reset on the swap until it is marked to market again or terminates. This procedure forces the party to which the swap is losing money to pay the other party before getting too deeply in debt.

Example

A two-year swap with semi-annual payments pays a floating rate and receives a fixed rate. The term structure at the beginning of the swap is L0(180) = 0.0583; L0(360) = 0.0616; L0(540) = 0.0680; L0(720) = 0.0705.

In order to mitigate the credit risk of the parties engaged in the swap, the swap will be marked to market in 180 days. Suppose it is now 180 days later and the swap is being marked to market. The new term structure is L180(180) = 0.0429; L180(360) = 0.0538; L180(540) = 0.0618.

The present value factors for 180, 360, 540 and 720 days are as follows:
B0(180) = 1/[1 + 0.0583 (180/360)] = 0.9717.
B0(360) = 1/[1 + 0.0616 (360/360)] = 0.9420.
B0(540) = 1/[1 + 0.0680 (540/360)] = 0.9074.
B0(720) = 1/[1 + 0.0705 (720/360)] = 0.8764.

The semi-annual fixed rate is calculated as (1 - 0.8764) / (0.9717 + 0.9420 + 0.9074 + 0.8764) = 0.0334.

The new present value factors are as follows:
B180(360) = 1/[1 + 0.0429 (180/360)] = 0.9790.
B180(540) = 1/[1 + 0.0538 (360/360)] = 0.9489.
B180(720) = 1/[1 + 0.0618 (540/360)] = 0.9152.

The present value of the remaining fixed payments plus the \$1 notional principal is 0.0334 x (0.9790 + 0.9489 + 0.9152) + 1 x 0.9152 = 1.0102.

Because we are on the payment date, the present value of the remaining floating payments plus hypothetical \$1 notional principal is automatically 1.0.

The market value of the swap to the pay-floating, receive-fixed party is 1.0102 - 1 = \$0.0102. Because the swap is marked to market, the party that pays floating will now receive \$0.0102 per \$1 of notional principal from the party that pays fixed. The two parties would then reprice the swap.

The new semi-annual fixed rate is calculated as (1 - 0.9152) / (0.9790 + 0.9489 + 0.9152) = 0.0298.

As in the futures market, marking a swap contract to market results in the two parties terminating the contract and automatically engaging in a new swap. In essence, the arrangement commits the two parties to terminating the swap and re-establishing it on a predetermined schedule.

#### Practice Question 1

Consider a two-year swap to pay a fixed rate and receive a floating rate with semi-annual payments. The fixed semi-annual rate is 0.0462. Now, 360 days later, the term structure is L360(180) = 0.101; L360(360) = 0.104.

The next floating payment will be 0.045. The swap calls for marking to market after 180 days, and, therefore, will now be marked to market. Which of the following statement is true?

Party A: pay fix and receive floating. Party B: receive fix and pay floating.

A. B pays A 0.0031 per \$1 of notional principal.
B. A pays B 0.0084 per \$1 of notional principal.
C. B pays B 0.0084 per \$1 of notional principal.

First find the discount factors:
B360(540) = 1/[1 + 0.101 x (180/360)] = 0.9519.
B360(720) = 1/[1 + 0.104 x (360/360)] = 0.9058.

The market value of the fixed payments plus hypothetical notional principal is 0.0462 (0.9519 + 0.9058) + 1.0 (0.9058) = 0.9916.

The market value of the floating payments plus \$1 hypothetical notional principal is 1.045 (0.9519) = 0.9947.

Therefore, the market value to the party paying fixed and receiving floating is 0.9947 - 0.9916 = 0.0031.

This amount would be paid by the party paying floating and receiving fixed.