## OI Term Rate

**is a direct subtype of Term Rate with functions OI Term Rate Functions, keys OI Term Rate keys and example object OiTermRt that represents an overnight index (oi) term rate**

*OI Term Rate***over a given period**

*R***, referred below as the "observation period".**

*[T₀,Tₙ]*The observation period is context-dependent and depends on the floating accrual period

**associated with the considered term rate**

*[Tₛ,Tₑ]*

*R*For example, a 5Y OIS usually has 5 floating accrual periods and each of them is associated with a corresponding oi term rate.

If one of these 5 periods is denoted as

**, the corresponding oi term rate**

*[Tₛ,Tₑ]***will have an observation period**

*R***that is constructed as described below.**

*[T₀,Tₙ]*First a reference period

**is constructed with its boundary dates**

*[T'₀,T'ₙ]***and**

*T'₀***as follows:**

*[T'₀,T'ₙ]***, where**

*T'₀ = Tₛ + δₛ***is a time interval that may be optionally defined as offset to the start date**

*δₛ***of the applicable floating accrual period**

*Tₛ*

*[Tₛ,Tₑ]***, where**

*T'ₙ = T* + δₑ***is a time interval that may be optionally defined as offset to the date**

*δₛ*

*T**Here the date

**depends on the time interval**

*T****specified in the entry Tenor**

*δ*If

**is defined,**

*δ*

*T* = T'₀ + δ*If

**is not defined,**

*δ***, where**

*T* = Tₑ***is the end date of the applicable floating accrual period**

*Tₑ*

*[Tₛ,Tₑ]*Then the final observation interval

**is constructed by shifting the**

*[T₀,Tₙ]***backwards by**

*[T'₀,T'ₙ]***business days specified in the entry Obs Lag**

*o***is defined as a certain average of the values of a referenced overnight rate**

*R***observed over**

*I*

*[T₀,Tₙ]*The type of average is specified by an element from the list Build Rule

In particular, assume the observation period consists of

**consecutive business dates**

*n+1***and for each**

*T₀, T₁,..., Tₙ***, the overnight value**

*i = 0,...,n-1***is assumed to apply on the interval**

*Iᵢ*

*[Tᵢ,Tᵢ₊₁]*The value

**may have been set prior to**

*Iᵢ*

*Tᵢ*In fact, if the overnight index

**has an inherent fixing lag period of**

*I***business days, the value**

*ε***will have been set on**

*Iᵢ*

*Tᵢ-ε*If an additional so called "lookback" period

**is specified in the entry Lookback, the value**

*λ***will have been set on**

*Iᵢ*

*Tᵢ-ε-λ***'s definition depends on the selected type of average.**

*R*In the Compound case,

**is defined as:**

*R*

*R = [Π(1+IᵢΔᵢ) - 1] / Δt*In the Average case,

**is defined as:**

*R*

*R = [Σ(IᵢΔᵢ)] / Δt*Above,

**is the product over all**

*Π***and**

*i***is the sum over all**

*Σ***, in both cases for**

*i*

*i = 0,...,n-1***is the length of the interval**

*Δᵢ***in annual units**

*[Tᵢ,Tᵢ₊₁]***is the period's**

*Δt***length in annual units**

*[T₀,Tₙ]*The following feature is also supported:

Rate Cutoff