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Yield_Curve_Bnd__VaR_Type__By_Rate

The Value At Risk of a tradable with respect to the market bond prices contained in the referenced yield curve is calculated by assuming that the underlying simulated risk factor applies to the bond yield y rather than the clean price B of each involved bond.
Due to the fact that bond yields are similar to other market rates, such as deposit or swap rates, this choice results in grouping bonds together with other rate instruments, when the risk factor affects a whole group.
For example, when the
VaR Spec::Buckets Treatment of the respective risk factor is VaR Spec::Buckets Treatment::Parallel, then a single risk factor suffices for moving in a parallel sense all market quotes of an ultimately rate type that include the bond price quotes, since the latter are represented by their yield y.
The moved bond prices are then recovered from the moved yields as follows:

If the
VaR Spec::Modelled Factor of the respective risk factor is VaR Spec::Modelled Factor::Shift, the risk factor equals a shift δ that gives the moved yield y' from the initial yield y according to:
y' = y + Ξ΄
The initial clean bond price B is moved to a new price B' according to a new shift Δ so that:
B' = B + Ξ”
Δ can be calculated as follows:
The definition of the modified duration D as D = -(1/B)dB/dy implies: dB = -DBdy
Approximating dB = Ξ” and dy = Ξ΄, the following final formula is produced:

Ξ” = -DBΞ΄

If the
VaR Spec::Modelled Factor of the respective risk factor is VaR Spec::Modelled Factor::Multiplier, the risk factor equals a multiplier m that gives the moved yield y' from the initial yield y according to:
y' = my
The initial clean bond price B is moved to a new price B' according to a new multiplier M so that:
B' = MB
M can be calculated as follows:
The definition of the modified duration D as D = -(1/B)dB/dy implies: dB = -DBdy
Writing dB = (M-1)B and dy = (m-1)y, the following final formula is produced:

M = 1-Dy(m-1)

Both D and y are calculated with respect to the settlement date of the respective bond and using the ACT/365F and Compounded conventions.