## By Rate

Subtype of VaR TypeThe Value At Risk of a tradable with respect to the market futures prices contained in the referenced yield curve is calculated by assuming that the underlying simulated risk factor applies to the interest rate

**rather than the futures price**

*R***of each involved futures contract.**

*F*Here

**is defined through**

*R*

*F = 100(1 - R)*Due to the fact that

**can be treated in the same fashion as other market rates, such as deposit or swap rates, this choice results in grouping futures together with other rate instruments, when the risk factor affects a whole group.**

*R*For example, when the Buckets Treatment of the respective risk factor is Parallel, then a single risk factor suffices for moving in a parallel sense all market quotes of an ultimately rate type, that include the futures price quotes, since the latter are represented by their equivalent rate

**.**

*R*The moved futures prices are then recovered from the moved

**as follows:**

*R*If the Modelled Factor of the respective risk factor is Shift, the risk factor equals a shift

**that gives the moved rate**

*δ***from the initial rate**

*R'***according to:**

*R*

*R' = R + δ*The initial futures price

**is moved to a new price**

*F***according to a new shift**

*F'***so that:**

*Δ*

*F' = F + Δ***can be calculated by differentiating the formula**

*Δ*

*F = 100(1 - R)*

*dF = -100dR*Approximating

**and**

*dF = Δ***, the following final formula is produced:**

*dR = δ*

*Δ = -100δ*If the Modelled Factor of the respective risk factor is Multiplier, the risk factor equals a multiplier

**that gives the moved rate**

*m***from the initial rate**

*R'***according to:**

*R*

*R' = mR*The initial futures price

**is moved to a new price**

*F***according to a new multiplier**

*F'***so that:**

*M*

*F' = MF***can be calculated as follows:**

*M*If

**then**

*R -> R' = mR*

*F -> F' = 100(1-R') = 100(1-mR)*If we set

**, the following final formula is produced:**

*F' = MF*

*M = 100(1-m)/F + m*