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 Equity Delta Sensitivities Equity 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 Equity Delta Risk Weight Equity 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 Equity Delta Risk Position Correlations Correlation parameter ρ k l \rho_{kl} ρ k l
Equity 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 ) Equity 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 Equity Vega Sensitivities Equity 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 Equity 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% ] Equity 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 This measure contributes the cross-product term that appears under the square root of the bucket-level charge formula K b K_b K b
Equity Vega Risk Position Correlations Formula ρ k l = m i n [ ρ k l D E L T A ⋅ ρ k l o p t i o n m a t u r i t y ; 1 ] \rho_{kl}=min\left [\rho_{kl}^{DELTA} \cdot \rho_{kl}^{option\ maturity};1 \right ] ρ k l = min [ ρ k l D E L T A ⋅ ρ k l o pt i o n ma t u r i t y ; 1 ] Correlation parameter ρ k l \rho_{kl} ρ k l
Equity 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 ) Equity 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 Equity Curvature Delta Sensitivities This measure matches Equity Delta Sensitivities for trades and risk factors having curvature risk charges.
Equity 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 Equity Delta Sensitivities for trades and risk factors having curvature risk charges.
Equity Curvature shock-up prices Equity Curvature shock-down prices Equity 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 Equity Curvature CVR Up can be replicated with these measures: Equity Curvature shock-up prices minus Equity Curvature Delta Weighted Sensitivities .
Equity 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 Equity Curvature CVR Down can be replicated with these measures: Equity Curvature shock-down prices plus Equity Curvature Delta Weighted Sensitivities .
Equity Curvature CVR The measure Equity Curvature CVR can be replicated by selecting either the Equity Curvature CVR Up or Equity Curvature CVR Down based on the scenario value of Equity Curvature Bucket Scenario .
Equity 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 + ) ) Equity 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 − ) ) Equity Curvature Risk Position Scenario Equity 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 − ) Equity Curvature Bucket Scenario The measure Equity Curvature Bucket Scenario can be replicated by evaluating Equity Curvature Risk Position Scenario at the Equity Buckets level.
Equity 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 Equity Curvature Risk Weight Equity 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 ) ) 
