## Rolldown

Function

**within IRS with keys IRS Rolldown keys returns the rolldown**

*Rolldown***of the referenced swap between the trade date**

*RD***and a horizon date**

*T₀***, with**

*Tʰ***in a given market environment defined by a discounting and forecasting curve represented as objects of type Yield Curve**

*T₀ < Tʰ*Web blog examples here and here

Here the rolldown

**is defined like in Bloomberg, as this screenshot shows:**

*RD*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

**is the swap's fair rate as of**

*r₀***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.**

*T₀***is the fair rate as of**

*rˢʰ***of a shortened swap that starts at the same time as the original swap, but matures at the earlier time**

*T₀***, where**

*Tˢʰ*

*Tˢʰ = Tᵐ - Δʰ*Here

**is the maturity date of the original swap and**

*Tᵐ***is the time interval from**

*Δʰ = Tʰ - T₀***to the horizon date**

*T₀*

*Tʰ*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

**and**

*clean***treatment.**

*dirty*By default, the

**is used if the key**

*clean treatment***is not specified.**

*Clean Terms*