## Stub Indices

Key

**in FxdIbor IRS refers to an optional 1D-array of objects of type Ibor Rate that define the additional reference indices - beyond the one defined in Ibor Index - used to construct the interpolated index**

*Stub Indices***that applies exclusively to the first period of the floating leg if that period is a short stub period, i.e. shorter than the tenor of the ibor index Ibor Index**

*r₀***is internally represented as a Swap Spread Rate and effectively equals the weighted average**

*r₀***, where**

*w₁r₁ + w₂r₂***are two ibor indices, of which the tenors either envelope or are closest to that of the first period.**

*r₁, r₂*Specifically, the

**are chosen from the indices supplied here and the one in Ibor Index so that it holds:**

*r₁, r₂*Case A:

*L₁ <= L₀ <= L₂*or in the special case where

**is smaller than any of the available tenors:**

*L₀*Case B:

*L₀ < L₁ < L₂*where

**is the length in calendar days of the tenor of the shorter ibor index**

*L₁*

*r₁***is the length in calendar days of the tenor of the longer ibor index**

*L₂*

*r₂***is the length in calendar days of the tenor of the first (stub) period of the floating leg.**

*L₀*In the case A, the weights

**are calculated as follows:**

*w₁, w₂*

*w₁ = (L₂ - L₀) / (L₂ - L₁)*

*w₂ = 1 - w₁*In the case B, the weights are:

*w₁ = 1*

*w₂ = 0*The so calculated

**are displayed as part of the first index of the parent element Index_2**

*r₁, r₂, w₁, w₂*