Equity and Total Return Swaps
Value an equity swap between settlement dates against a fixed, floating or second equity leg, find the index level at which it is worth zero, and work out one period's net payment.
Learning focus: holding the index from the last settlement replicates the equity leg, so it is worth notional × S_t ÷ S_last today, and the swap's value is that less the other leg valued as a bond.
The period runs from the last settlement, at the index level above. The other leg's payment uses the first payment date's τ.
The fixed leg is valued as a bond: each coupon (notional × rate × τ) plus the notional on the last date, discounted at that date's DF.
The value is a straight line in the index level: each point the index moves changes the equity leg by notional ÷ S_last, while the other leg stays put.