Swaps and forward swaps

A plain vanilla interest rate swap is an agreement between two counterparties to
exchange a stream of fixed interest rate payments for a stream of floating interest
rate payments. Both streams are denominated in the same currency and are based
on a notional principal amount. The notional principal is not exchanged. The design
of a swap has three features that determine its price: the maturity of the swap, the
maturity of the floating rate, and the frequency of payments. We will assume for
expository purposes that the latter two features coincide, e.g. if the swap design is
fixed against six-month Libor, then payments are exchanged semiannually.
At initiation, the price of a plain-vanilla swap is set so its current value – the net
value of the two interest payment streams, fixed and floating – is zero. The swap can
be seen as a portfolio which, from the point of view of the payer of fixed interest
(called the ‘payer’ in market parlance) is long a fixed-rate bond and short a floatingrate
bond, both in the amount of the notional principal. The payer of floating-rate
interest (called the ‘receiver’ in market parlance) is long the floater and short the
fixed-rate bond.
The price of a swap is usually quoted as the swap rate, that is, as the yield to
maturity on a notional par bond. What determines this rate? A floating-rate bond
always trades at par at the time it is issued. The fixed-rate bond, which represents
the payer’s commitment in the swap, must then also trade at par if the swap is to
have an initial value of zero. In other words, the swap rate is the market-adjusted
yield to maturity on a par bond.
Swap rates are also often quoted as a spread over the government bond with a
maturity closest to that of the swap. This spread, called the swap-Treasury spread,
is almost invariably positive, but varies widely in response to factors such as liquidity
and risk appetites in the fixed-income markets.
A forward swap is an agreement between two counterparties to commence a swap
at some future settlement date. As in the case of a cash swap, the forward swap rate
is the market-adjusted par rate on a coupon bond issued at the settlement date. The
rate on a forward swap can be calculated from forward rates or spot rates.