Each subsection below lists the risk weight, sensitivities, risk position, and risk charge measures for the corresponding calculation stage. Jump to the relevant section:
Required hierarchies must be present in the query for the measure to evaluate correctly.
Delta GIRR Delta Sensitivities GIRR Delta Weighted Sensitivities Formula W S k = R W k ⋅ s k WS_k=RW_k \cdot s_k W S k = R W k ⋅ s k GIRR Delta Risk Weight GIRR Delta Risk Position Double Sums Formula ∑ k ∈ b ∑ l ∈ b ⋅ W S k ⋅ W S l \sum _{k\in b}\sum _{l\in b}\cdot WS_k \cdot WS_l ∑ k ∈ b ∑ l ∈ b ⋅ W S k ⋅ W S l GIRR Delta Risk Position Correlations Correlation parameter ρ k l \rho_{kl} ρ k l
GIRR Delta Risk Position Formula K b = m a x ( 0 , ∑ k ∈ b W S k 2 + ∑ k ∈ b ∑ l ∈ b , l ≠ k ρ k l ⋅ W S k ⋅ W S l ) K_{b} =\sqrt{max \left( 0, \sum _{k\in b} WS_{k}^{2} +\sum _{k\in b}\sum _{l\in b, l\neq k}\rho_{kl}\cdot WS_k \cdot WS_l\right)} K b = ma x ( 0 , ∑ k ∈ b W S k 2 + ∑ k ∈ b ∑ l ∈ b , l = k ρ k l ⋅ W S k ⋅ W S l ) GIRR Delta Risk Charge Formula K = ∑ b K b 2 + ∑ b ∑ c ≠ b γ b c ⋅ S b ⋅ S c where S b = ∑ k W S k if ∑ b K b 2 + ∑ b ∑ c ≠ b γ b c ⋅ K b ⋅ K c > 0 else S b = m a x ( m i n ( ∑ k W S k , K b ) , − K b ) \begin{aligned}
&K = \sqrt{\sum _{b} K_{b}^{2} + \sum _{b}\sum _{c\neq b}\gamma_{bc}\cdot S_b \cdot S_c} \\
&\text{where } S_b = \sum _{k} WS_k \text{ if } \sum _{b} K_{b}^{2} + \sum _{b}\sum _{c\neq b}\gamma_{bc}\cdot K_b \cdot K_c > 0 \\
&\text{else } S_b = max(min(\sum _{k} WS_k, K_b), -K_b)
\end{aligned} K = b ∑ K b 2 + b ∑ c = b ∑ γ b c ⋅ S b ⋅ S c where S b = k ∑ W S k if b ∑ K b 2 + b ∑ c = b ∑ γ b c ⋅ K b ⋅ K c > 0 else S b = ma x ( min ( k ∑ W S k , K b ) , − K b ) Vega GIRR Vega Sensitivities GIRR Vega Weighted Sensitivities Formula W S k = R W k ⋅ s k WS_k=RW_k \cdot s_k W S k = R W k ⋅ s k GIRR Vega Risk Weight Formula R W k = min [ R W σ ⋅ L H r i s k c l a s s 10 ; 100 % ] RW_k = \min\left[RW_\sigma \cdot \frac{\sqrt{LH_{riskclass}}}{\sqrt{10}}; 100\%\right] R W k = min [ R W σ ⋅ 10 L H r i s k c l a ss ; 100% ] GIRR Vega Risk Position Double Sums Formula ∑ k ∈ b ∑ l ∈ b ⋅ W S k ⋅ W S l \sum _{k\in b}\sum _{l\in b}\cdot WS_k \cdot WS_l ∑ k ∈ b ∑ l ∈ b ⋅ W S k ⋅ W S l Sum of cross product of the weighted sensitivities under the square root in the bucket-level charge formula K b K_b K b
GIRR Vega Risk Position Correlations Correlation parameter ρ k l \rho_{kl} ρ k l
GIRR Vega Risk Position Formula K b = m a x ( 0 , ∑ k ∈ b W S k 2 + ∑ k ∈ b ∑ l ∈ b , l ≠ k ρ k l ⋅ W S k ⋅ W S l ) K_{b} =\sqrt{max \left( 0, \sum _{k\in b} WS_{k}^{2} +\sum _{k\in b}\sum _{l\in b, l\neq k}\rho_{kl}\cdot WS_k \cdot WS_l\right)} K b = ma x ( 0 , ∑ k ∈ b W S k 2 + ∑ k ∈ b ∑ l ∈ b , l = k ρ k l ⋅ W S k ⋅ W S l ) GIRR Vega Risk Charge Formula K = ∑ b K b 2 + ∑ b ∑ c ≠ b γ b c ⋅ S b ⋅ S c where S b = ∑ k W S k if ∑ b K b 2 + ∑ b ∑ c ≠ b γ b c ⋅ K b ⋅ K c > 0 else S b = m a x ( m i n ( ∑ k W S k , K b ) , − K b ) \begin{aligned}
&K = \sqrt{\sum _{b} K_{b}^{2} + \sum _{b}\sum _{c\neq b}\gamma_{bc}\cdot S_b \cdot S_c} \\
&\text{where } S_b = \sum _{k} WS_k \text{ if } \sum _{b} K_{b}^{2} + \sum _{b}\sum _{c\neq b}\gamma_{bc}\cdot K_b \cdot K_c > 0 \\
&\text{else } S_b = max(min(\sum _{k} WS_k, K_b), -K_b)
\end{aligned} K = b ∑ K b 2 + b ∑ c = b ∑ γ b c ⋅ S b ⋅ S c where S b = k ∑ W S k if b ∑ K b 2 + b ∑ c = b ∑ γ b c ⋅ K b ⋅ K c > 0 else S b = ma x ( min ( k ∑ W S k , K b ) , − K b ) Curvature GIRR Curvature Delta Sensitivities This measure matches GIRR Delta Sensitivities for trades and risk factors having curvature risk charges.
GIRR Curvature Delta Weighted Sensitivities Formula R W k ( c u r v a t u r e ) ⋅ s i k RW_k^{(curvature)} \cdot s_{ik} R W k ( c u r v a t u re ) ⋅ s ik This measure matches GIRR Delta Sensitivities for trades and risk factors having curvature risk charges.
GIRR Curvature shock-up prices GIRR Curvature shock-down prices GIRR Curvature CVR Up Formula − ∑ i { V i ( x k ( R W ( c u r v a t u r e ) + ) ) − V i ( x k ) − R W k ( c u r v a t u r e ) ⋅ s i k ) } -\sum_{i}\left \{ V_i\left ( x_k^{(RW^{(curvature)+})} \right ) -V_i(x_k)-RW_k^{(curvature)}\cdot s_{ik})\right \} − ∑ i { V i ( x k ( R W ( c u r v a t u re ) + ) ) − V i ( x k ) − R W k ( c u r v a t u re ) ⋅ s ik ) } The measure GIRR Curvature CVR Up can be replicated with these measures: GIRR Curvature shock-up prices minus GIRR Curvature Delta Weighted Sensitivities .
GIRR Curvature CVR Down Formula − ∑ i { V i ( x k ( R W ( c u r v a t u r e ) − ) ) − V i ( x k ) + R W k ( c u r v a t u r e ) ⋅ s i k ) } -\sum_{i}\left \{ V_i\left ( x_k^{(RW^{(curvature)-})} \right ) -V_i(x_k)+RW_k^{(curvature)}\cdot s_{ik})\right \} − ∑ i { V i ( x k ( R W ( c u r v a t u re ) − ) ) − V i ( x k ) + R W k ( c u r v a t u re ) ⋅ s ik ) } The measure GIRR Curvature CVR Down can be replicated with these measures: GIRR Curvature shock-down prices plus GIRR Curvature Delta Weighted Sensitivities .
GIRR Curvature CVR The measure GIRR Curvature CVR can be replicated by selecting either the GIRR Curvature CVR Up or GIRR Curvature CVR Down based on the scenario value of GIRR Curvature Bucket Scenario .
GIRR Curvature Risk Position Up Formula K b + = m a x ( 0 , ∑ k ∈ b m a x ( C V R k + , 0 ) 2 + ∑ k ∈ b ∑ l ∈ b , l ≠ k ρ k l ⋅ C V R k + ⋅ C V R l + ⋅ ψ ( C V R k + , C V R l + ) ) K_{b}^{+} =\sqrt{max\left(0,\sum _{k\in b} max(CVR_k^{+},0)^{2} +\sum _{k\in b}\sum _{l\in b, l\neq k}\rho_{kl}\cdot CVR_k^{+} \cdot CVR_l^{+} \cdot \psi(CVR_k^{+},CVR_l^{+})\right)} K b + = ma x ( 0 , ∑ k ∈ b ma x ( C V R k + , 0 ) 2 + ∑ k ∈ b ∑ l ∈ b , l = k ρ k l ⋅ C V R k + ⋅ C V R l + ⋅ ψ ( C V R k + , C V R l + ) ) GIRR Curvature Risk Position Down Formula K b − = m a x ( 0 , ∑ k ∈ b m a x ( C V R k − , 0 ) 2 + ∑ k ∈ b ∑ l ∈ b , l ≠ k ρ k l ⋅ C V R k − ⋅ C V R l − ⋅ ψ ( C V R k − , C V R l − ) ) K_{b}^{-} =\sqrt{max\left(0,\sum _{k\in b} max(CVR_k^{-},0)^{2} +\sum _{k\in b}\sum _{l\in b, l\neq k}\rho_{kl}\cdot CVR_k^{-} \cdot CVR_l^{-} \cdot \psi(CVR_k^{-},CVR_l^{-})\right)} K b − = ma x ( 0 , ∑ k ∈ b ma x ( C V R k − , 0 ) 2 + ∑ k ∈ b ∑ l ∈ b , l = k ρ k l ⋅ C V R k − ⋅ C V R l − ⋅ ψ ( C V R k − , C V R l − ) ) GIRR Curvature Risk Position Scenario GIRR Curvature Risk Position Formula K b = m a x ( K b + , K b − ) K_b=max(K_b^{+},K_b^{-}) K b = ma x ( K b + , K b − ) GIRR Curvature Bucket Scenario The measure GIRR Curvature Bucket Scenario can be replicated by evaluating GIRR Curvature Risk Position Scenario at the GIRR Buckets level.
GIRR Curvature Sb Formula S b = ∑ k C V R k + when scenario is upward, S b = ∑ k C V R k − when scenario is downward S_b = \sum_k CVR_k^{+}\text{ when scenario is upward, } S_b = \sum_k CVR_k^{-}\text{ when scenario is downward} S b = ∑ k C V R k + when scenario is upward, S b = ∑ k C V R k − when scenario is downward GIRR Curvature Risk Weight GIRR Curvature Risk Charge Formula C u r v a t u r e r i s k = m a x ( 0 , ∑ b K b 2 + ∑ b ∑ c ≠ b γ b c ⋅ S b ⋅ S c ⋅ ψ ( S b , S c ) ) Curvature\ risk = \sqrt{max\left ( 0,\sum _{b} K_{b}^{2} + \sum _{b}\sum _{c\neq b}\gamma_{bc}\cdot S_b \cdot S_c \cdot \psi (S_b,S_c) \right )} C u r v a t u re r i s k = ma x ( 0 , ∑ b K b 2 + ∑ b ∑ c = b γ b c ⋅ S b ⋅ S c ⋅ ψ ( S b , S c ) ) 
