A swap is a series of cash flows on two legs. At the trade date (which is assumed to be the effective date, unless mentioned otherwise), a swap has a zero value, i.e., it is said to be an on-market swap (having a net present value of zero):
PV (fixed leg) + PV (floating leg) = 0
Over time, the cash flows on the two legs may mismatch, whereby producing an off-market swap. Generally, the floating leg is equal to the notional principal amount at each day of coupon settlement (based on a floating rate such as LIBOR). The fixed rate can be valued by a standard net present value calculation, since the paid amount is known for certain. In order to price interest rate swaps and currency swaps, banks and institutional investors usually use par swap pricing or zero-coupon swap pricing.
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