> ## Documentation Index
> Fetch the complete documentation index at: https://docs.activeviam.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Sensitivity level margin

### IM\_Commodity\_CurvatureMargin

|                 |                                                           |
| --------------- | --------------------------------------------------------- |
| **Description** | Margin aggregation from Commodity curvature sensitivities |
| **Notation**    | $CurvatureMargin_{RiskClass}$                             |

**Formula**

$CurvatureMargin =max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_Commodity\_DeltaMargin

|                 |                                                       |
| --------------- | ----------------------------------------------------- |
| **Description** | Margin aggregation from Commodity delta sensitivities |
| **Notation**    | $DeltaMargin_{RiskClass}$                             |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_Commodity\_VegaMargin

|                 |                                                      |
| --------------- | ---------------------------------------------------- |
| **Description** | Margin aggregation from Commodity vega sensitivities |
| **Notation**    | $VegaMargin_{RiskClass}$                             |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_CreditNonQ\_CurvatureMargin

|                 |                                                                       |
| --------------- | --------------------------------------------------------------------- |
| **Description** | Margin aggregation from Credit Non Qualifying curvature sensitivities |
| **Notation**    | $CurvatureMargin$                                                     |

**Formula**

$CurvatureMargin =max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_CreditNonQ\_DeltaMargin

|                 |                                                                   |
| --------------- | ----------------------------------------------------------------- |
| **Description** | Margin aggregation from Credit Non Qualifying delta sensitivities |
| **Notation**    | $DeltaMargin$                                                     |

**Formula**

$DeltaMargin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \ S_{b} \  S_{c}}} + K_{residual}$

### IM\_CreditNonQ\_VegaMargin

|                 |                                                                  |
| --------------- | ---------------------------------------------------------------- |
| **Description** | Margin aggregation from Credit Non Qualifying Vega sensitivities |
| **Notation**    | $VegaMargin$                                                     |

**Formula**

$VegaMargin =\sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{b \neq c} \gamma_{bc}} \ g_{{bc}} \ S_{b} \ S_{c}} + K_{residual}$

### IM\_CreditQ\_BaseCorrMargin

|                 |                                                                  |
| --------------- | ---------------------------------------------------------------- |
| **Description** | Margin aggregation from Credit Qualifying BaseCorr sensitivities |
| **Notation**    | $BaseCorrMargin$                                                 |

**Formula**

$BaseCorrMargin = \sqrt{\sum_{k}WS_{k}^{2} + \sum_{k}{\sum_{l \neq k}  \rho_{k,l} \cdot WS_{k} \cdot WS_{l}}}$

### IM\_CreditQ\_CurvatureMargin

|                 |                                                        |
| --------------- | ------------------------------------------------------ |
| **Description** | Margin aggregation from Credit curvature sensitivities |
| **Notation**    | $CurvatureMargin$                                      |

**Formula**

$CurvatureMargin =max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_CreditQ\_DeltaMargin

|                 |                                                    |
| --------------- | -------------------------------------------------- |
| **Description** | Margin aggregation from Credit delta sensitivities |
| **Notation**    | $DeltaMargin$                                      |

**Formula**

$DeltaMargin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \ S_{b} \  S_{c}}} + K_{residual}$

### IM\_CreditQ\_VegaMargin

|                 |                                                   |
| --------------- | ------------------------------------------------- |
| **Description** | Margin aggregation from Credit vega sensitivities |
| **Notation**    | $VegaMargin$                                      |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_Equity\_CurvatureMargin

|                 |                                                        |
| --------------- | ------------------------------------------------------ |
| **Description** | Margin aggregation from Equity curvature sensitivities |
| **Notation**    | $CurvatureMargin_{RiskClass}$                          |

**Formula**

$CurvatureMargin = CurvatureMargin_{non-residual} + CurvatureMargin_{residual}, \\ CurvatureMargin =max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_Equity\_DeltaMargin

|                 |                                                    |
| --------------- | -------------------------------------------------- |
| **Description** | Margin aggregation from Equity delta sensitivities |
| **Notation**    | $DeltaMargin_{RiskClass}$                          |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_Equity\_VegaMargin

|                 |                                                   |
| --------------- | ------------------------------------------------- |
| **Description** | Margin aggregation from Equity vega sensitivities |
| **Notation**    | $VegaMargin_{RiskClass}$                          |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_FX\_CurvatureMargin

|                 |                                                    |
| --------------- | -------------------------------------------------- |
| **Description** | Margin aggregation from FX curvature sensitivities |
| **Notation**    | $CurvatureMargin_{RiskClass}$                      |

**Formula**

$CurvatureMargin =max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_FX\_DeltaMargin

|                 |                                                |
| --------------- | ---------------------------------------------- |
| **Description** | Margin aggregation from FX delta sensitivities |
| **Notation**    | $DeltaMargin_{RiskClass}$                      |

**Formula**

$\text{FX DeltaMargin} = K_b$

### IM\_FX\_VegaMargin

|                 |                                               |
| --------------- | --------------------------------------------- |
| **Description** | Margin aggregation from FX vega sensitivities |
| **Notation**    | $VegaMargin_{RiskClass}$                      |

**Formula**

$\text{FX DeltaMargin} = K_b$

### IM\_IR\_CurvatureMargin

|                 |                                                           |
| --------------- | --------------------------------------------------------- |
| **Description** | Margin aggregation from Commodity curvature sensitivities |
| **Notation**    | $CurvatureMargin_{RiskClass}$                             |

**Formula**

$CurvatureMargin =HVR_{IR}^{-2} \cdot max\left ( \sum_{b,k} CVR_{b,k} + \lambda \cdot  \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c}^2  \cdot S_{b} \cdot S_{c}}} ,0 \right )$

### IM\_IR\_DeltaMargin

|                 |                                                |
| --------------- | ---------------------------------------------- |
| **Description** | Margin aggregation from IR delta sensitivities |
| **Notation**    | $DeltaMargin_{RiskClass}$                      |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$

### IM\_IR\_VegaMargin

|                 |                                               |
| --------------- | --------------------------------------------- |
| **Description** | Margin aggregation from IR vega sensitivities |
| **Notation**    | $VegaMargin_{RiskClass}$                      |

**Formula**

$Margin = \sqrt{\sum_{b}K_{b}^{2} + \sum_{b}{\sum_{c \neq b} \gamma_{b,c} \cdot g_{b,c} \cdot S_{b} \cdot S_{c}}} + K_{residual}$