Separating Forward Curve from Discount Curve
The previous two chapters presented the standard treatment of building swap curves from traded instruments. Alongside plain-vanilla swaps, there is another class of floating-for-floating swaps, referred to as money-market basis swaps or simply basis swaps, where both legs of the swap are floating, but based on different short term (money-market) interest-rate indices.
Pricing and risk management of basis swaps is more nuanced than plain-vanillas. For one reason, the primary risk captured by them is the credit risk between the indices, say Government (Fed-Funds) versus Bank (Libor) credit. They also at times represent supply-demand dynamics of one index versus another one, independent of the inherent credit risk in each index. In order to provide a consistent framework to price them, one has to step back from the previous setup, where a single discount factor curve captured both discounting and calculation of forward rates, as basis swaps provide independent information about the forward/locking curve of an index, separate from the discount (funding) curve.
FORWARD CURVES FOR ASSETS
We have so far presented forward prices and rates in specialized instances. It will help to step back, and provide a generic definition of a forward contract. At a given time t, the value of an asset A for spot (cash) delivery is obviously A(t). However, if we need the asset only at some future time T > t, then we can enter into a forward ...