Shorten Spot
Subtype of DefinitionThe shortened swap from the trade dateT₀ to the shortened maturity Tˢʰ - as described in the function Rolldown - is constructed by keeping the original swap as it is until the date Tˢʰ and chop off the rest, thereby assuming that the terminal cash flows are paid at Tˢʰ
Here Tˢʰ = Tᵐ - Δʰ and Δʰ = Tʰ - T₀
This definiton of constructing the shortened swap has the advantage that the produced time structure is identical with that of the original swap until Tʰ and thus cannot result in new reset dates occurring before T₀
On the other hand, it is incorrect as it does not capture the economic meaning of rolldown which relates to the part of the structure of the swap that lies beyond Tʰ
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 Fwd as Spot in the case of a 5Y spot OIS with a 3M horizon.
