Fwd as Spot
Subtype of DefinitionThe shortened swap from the trade dateT₀ to the shortened maturity Tˢʰ - as described in the function Rolldown - is constructed by dragging the forward swap starting at the horizon date Tʰ to the left by the interval Δ
Here Tˢʰ = Tᵐ - Δʰ and Δʰ = Tʰ - T₀
The forward swap - before being dragged to the left - is assumed to have been constructed in either clean or dirty terms, in accordance with the entry in key Clean Terms
When viewed from T₀, the resulting swap looks similar to how the forward swap would have looked, had it been viewed from Tʰ
Dragging the forward swap bakwards in time may result in the reset date of the floating leg's first period to be dragged to some date prior to T₀
In such a case, the reset date is moved to T₀ so that the associated fixing can be implied by the given forecasting curve.
This shortened swap definition affects the calculated fair rate rˢʰ and thus the returned rolldown RD
Below is a diagram that demonstrates this treatment against that of Shorten Spot in the case of a 5Y spot OIS with a 3M horizon.
