> ## 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.

# Curvature

### IM\_IR\_CurvatureMargin\_Partial

|                 |                                                                                                  |
| --------------- | ------------------------------------------------------------------------------------------------ |
| **Description** | Margin aggregation from interest rate curvature sensitivities before applying the HVR multiplier |

**Formula**

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

### Lambda\_Commodity

|                 |                                                      |
| --------------- | ---------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation |
| **Notation**    | $\lambda$                                            |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_CreditNonQ\_Non-residual

|                 |                                                                             |
| --------------- | --------------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - non-residual buckets |
| **Notation**    | $\lambda$                                                                   |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_CreditNonQ\_residual

|                 |                                                                         |
| --------------- | ----------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - residual buckets |
| **Notation**    | $\lambda$                                                               |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_CreditQ\_Non-residual

|                 |                                                                             |
| --------------- | --------------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - non-residual buckets |
| **Notation**    | $\lambda$                                                                   |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_CreditQ\_residual

|                 |                                                                         |
| --------------- | ----------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - residual buckets |
| **Notation**    | $\lambda$                                                               |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_Equity\_Non-residual

|                 |                                                                         |
| --------------- | ----------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - residual buckets |
| **Notation**    | $\lambda$                                                               |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### LAMBDA\_Equity\_residual

|                 |                                                                         |
| --------------- | ----------------------------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation - residual buckets |
| **Notation**    | $\lambda$                                                               |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### Lambda\_FX

|                 |                                                      |
| --------------- | ---------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation |
| **Notation**    | $\lambda$                                            |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### Lambda\_IR

|                 |                                                      |
| --------------- | ---------------------------------------------------- |
| **Description** | Lambda parameter in the curvature margin aggregation |
| **Notation**    | $\lambda$                                            |

**Formula**

$\lambda =( \left ( \Phi_{99.5}^{-1} \right )^2-1)(1+\theta)-\theta$

### Theta\_Commodity

|                 |                                                     |
| --------------- | --------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation |
| **Notation**    | $\theta$                                            |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_CreditNonQ\_Non-residual

|                 |                                                                           |
| --------------- | ------------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - non-residual bucket |
| **Notation**    | $\theta$                                                                  |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_CreditNonQ\_residual

|                 |                                                                       |
| --------------- | --------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - residual bucket |
| **Notation**    | $\theta$                                                              |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_CreditQ\_Non-residual

|                 |                                                                           |
| --------------- | ------------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - non-residual bucket |
| **Notation**    | $\theta$                                                                  |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_CreditQ\_residual

|                 |                                                                       |
| --------------- | --------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - residual bucket |
| **Notation**    | $\theta$                                                              |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_Equity\_Non-residual

|                 |                                                                           |
| --------------- | ------------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - non-residual bucket |
| **Notation**    | $\theta$                                                                  |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### THETA\_Equity\_residual

|                 |                                                                       |
| --------------- | --------------------------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation - residual bucket |
| **Notation**    | $\theta$                                                              |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### Theta\_FX

|                 |                                                     |
| --------------- | --------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation |
| **Notation**    | $\theta$                                            |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$

### Theta\_IR

|                 |                                                     |
| --------------- | --------------------------------------------------- |
| **Description** | Theta parameter in the curvature margin aggregation |
| **Notation**    | $\theta$                                            |

**Formula**

$\theta = min\left ( \frac{\sum_{b,k} CVR_{b,k}}{\sum_{b,k}|CVR_{b,k}|} ,0\right )$