> ## 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.

# Bucket level margin

### K\_Commodity\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Commodity curvature sensitivities              |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_Commodity\_DeltaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Commodity delta sensitivities                  |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} WS_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot WS_{k} \cdot WS_{l} }$

### K\_Commodity\_VegaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Commodity vega sensitivities                   |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} VR_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot VR_{k} \cdot VR_{l} }$

### K\_CreditNonQ\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Credit Non-Qualifying curvature sensitivities  |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_CreditNonQ\_DeltaMargin

|                 |                                                                   |
| --------------- | ----------------------------------------------------------------- |
| **Description** | Bucket-level margin for Credit Non Qualifying Delta sensitivities |
| **Notation**    | $K$                                                               |

**Formula**

$K =\sqrt{\sum_{k}WS_{k}^{2} + \sum_{k}{\sum_{k \neq l} \rho_{kl}} \ WS_{k} \ WS_{l}}$

### K\_CreditNonQ\_VegaMargin

|                 |                                                                  |
| --------------- | ---------------------------------------------------------------- |
| **Description** | Bucket-level margin for Credit Non Qualifying Vega sensitivities |
| **Notation**    | $K_{b}$                                                          |

**Formula**

$K_{b} =\sqrt{\sum_{k}VR_{k}^{2} + \sum_{k}{\sum_{k \neq l} \rho_{kl}} \ f_{kl} \ VR_{k} \ VR_{l}}$

### K\_CreditQ\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Credit Qualifying curvature sensitivities      |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_CreditQ\_DeltaMargin

|                 |                                                               |
| --------------- | ------------------------------------------------------------- |
| **Description** | Margin aggregation from Credit Qualifying Delta sensitivities |
| **Notation**    | $K$                                                           |

**Formula**

$K =\sqrt{\sum_{k}WS_{k}^{2} + \sum_{k}{\sum_{k \neq l} \rho_{kl}} \ WS_{k} \ WS_{l}}$

### K\_CreditQ\_VegaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Credit Qualifying vega sensitivities           |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} VR_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot VR_{k} \cdot VR_{l} }$

### K\_Equity\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Equity curvature sensitivities                 |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_Equity\_DeltaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Equity delta sensitivities                     |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} WS_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot WS_{k} \cdot WS_{l} }$

### K\_Equity\_VegaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for Equity vega sensitivities                      |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} VR_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot VR_{k} \cdot VR_{l} }$

### K\_FX\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for FX curvature sensitivities                     |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_FX\_DeltaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for FX delta sensitivities                         |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} WS_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot WS_{k} \cdot WS_{l} }$

### K\_FX\_VegaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for FX vega sensitivities                          |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} VR_{k}^{2} + \sum_{k} \sum_{l \neq k} f_{k,l} \cdot \rho_{k,l} \cdot VR_{k} \cdot VR_{l} }$

### K\_Generic

|                 |                                                              |
| --------------- | ------------------------------------------------------------ |
| **Description** | Sum of Bucket-level margins across sensitivities and buckets |

### K\_IR\_CurvatureMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for IR curvature sensitivities                     |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} CVR_{k}^{2} + \sum_{k} \sum_{l \neq k} \rho_{k,l}^2 \cdot CVR_{k} \cdot CVR_{l} }$

### K\_IR\_DeltaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for IR delta sensitivities                         |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k,i \in b} WS_{k,i}^{2} + \sum_{k,i} \sum_{(j,l) \neq (k,i)} \phi_{i,j} \cdot \rho_{kl} \cdot WS_{k,i} \cdot WS_{l,j} }$

### K\_IR\_VegaMargin

|                          |                                                                        |
| ------------------------ | ---------------------------------------------------------------------- |
| **Description**          | Bucket-level margin for IR vega sensitivities                          |
| **Notation**             | $K_b$                                                                  |
| **Required hierarchies** | [RegulatoryBuckets](../dimensions/regulatorybuckets#regulatorybuckets) |

**Formula**

$K_{b} = \sqrt{\sum_{k \in b} VR_{k}^{2} + \sum_{k} \sum_{l \neq k}  \rho_{k,l} \cdot VR_{k} \cdot VR_{l} }$