Rolldown


Function Rolldown within
IRS with keys IRS Rolldown keys returns the rolldown RD of the referenced swap between the trade date T₀ and a horizon date , with T₀ < Tʰ in a given market environment defined by a discounting and forecasting curve represented as objects of type Yield Curve

Web blog examples
here and here

Here the rolldown RD is defined like in Bloomberg, as this screenshot shows:



Accordingly, RD is calculated as the par rate from swap start to maturity minus the par rate from start to (maturity minus horizon date), in bps per annum.

Formally:
RD = r₀ - rˢʰ
where
r₀ is the swap's fair rate as of T₀ using the supplied yield curves, which is defined as the rate the swap's fixed leg ought to have so that its PV at T₀ to equal 0.
rˢʰ is the fair rate as of T₀ of a shortened swap that starts at the same time as the original swap, but matures at the earlier time Tˢʰ, where Tˢʰ = Tᵐ - Δʰ
Here Tᵐ is the maturity date of the original swap and Δʰ = Tʰ - T₀ is the time interval from T₀ to the horizon date

In Deriscope, the above definiton is tweaked somewhat and splits into three alternative definitions that result in different rates rˢʰ
These definitions can be selected through the optional key
Definition

Download the workbooks
irs-carryroll.xlsx and ois-carryroll.xlsx that demonstrate both methods described here.

Similar to the
Carry case, the optional key Clean Terms can be used to choose between the clean and dirty treatment.
By default, the clean treatment is used if the key Clean Terms is not specified.