Valuing the Swap

Net Cash Flows

Netting the legs period by period gives the same value.

highlighted = computed this step

Net each period

For the fixed payer, each period's net receipt is notional times forward rate minus fixed rate. With fixed rate 5%, the exact net receipts are minus 250/3 cents, 500/3 cents, and 1500/7 cents.

nett=N(ft−K)\text{net}_t=N(f_t-K)

Discount the net flows

Displayed to cents, those net receipts are $-0.83, $1.67, and $2.14. Discounting the exact net receipts gives total value $2.50.

∑t=1nN(ft−K)dt=$2.50\sum_{t=1}^n N(f_t-K)d_t=\$2.50
Fixed-payer net cash flowsNet receipts are discounted with the same curve.Fixed-payer net valuePeriodForward - fixedNet receiptDiscount factorPV of net11/24 - 1/20-250/3 cents ($-0.83)24/25$-0.8021/15 - 1/20500/3 cents ($1.67)9/10$1.5031/14 - 1/201500/7 cents ($2.14)21/25$1.80Swap value$+2.50

Same value, two views

The leg-value view and the net-cash-flow view are the same computation under the stated curve. This is descriptive, not investment advice.

PV of legs=PV of net flows\text{PV of legs}=\text{PV of net flows}