OI Term Rate
OI Term Rate is a direct subtype of Term Rate
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE OI Term Rate
This type represents an overnight index (oi) term rate R calculated based on the daily interest accrued by certain overnight rates over a given calculation period [T₀,Tₙ].
The calculation period is context-dependent and depends on the floating accrual period [Tₛ,Tₑ] associated with the considered term rate 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 [Tₛ,Tₑ] based on a start date Tₛ and an end date Tₑ, the corresponding oi term rate R will have a calculation period [T₀,Tₙ] that is constructed as described below.
First a reference period [T'₀,T'ₙ] is constructed with its boundary dates T'₀ and T'ₙ as follows:
T'₀ = Tₛ + δₛ, where δₛ is a time interval that may be optionally defined as offset to the start date Tₛ of the applicable floating accrual period [Tₛ,Tₑ]
T'ₙ = T* + δₑ, where δₑ is a time interval that may be optionally defined as offset to the date T*
Here the date T* depends on the time interval Δ specified in the entry Tenor
If Δ is defined, T* = T'₀ + Δ
If Δ is not defined, T* = Tₑ
Then the final calculation period [T₀,Tₙ] is constructed by shifting the reference period [T'₀,T'ₙ] backwards by o business days specified in the entry Obs Lag
The calculation period's start and end dates are denoted by T₀ and Tₙ because that period will be divided into n consecutive subintervals along a sequence of dates T₀, T₁,..., Tₙ, as explained below.
In the absence of lookback (explained below), R is defined as a certain average of the values of a referenced overnight index I observed on the business days of the interval [T₀,Tₙ].
I could be the SOFR index in the US, the ESTER index in the Euro zone or any other sort of overnight rate.
The type of average is specified by an element from the list Build Rule
In particular, assume the calculation period contains n+1 consecutive business dates T₀, T₁,..., Tₙ and for each i = 0,...,n-1, the value Iᵢ denotes the published fixing of the index I as set on or prior to Tᵢ
In fact, if the overnight index I has an inherent fixing lag period of ε business days, the value Iᵢ will have been set on Tᵢ-ε
But if a so called "lookback" period λ is specified in the entry Lookback, the value Iᵢ will have been set on Tᵢ-λ
Regardless of whether Iᵢ is set on or before Tᵢ, both definitions below assume that its corresponding accrual period is the interval [Tᵢ,Tᵢ₊₁]
R's definition depends on the selected type of average.
In the Compound case, R is defined as:
R = [Π(1+Iᵢτᵢ) - 1] / τ
In the Average case, R is defined as:
R = [Σ(Iᵢτᵢ)] / τ
Above, Π is the product over all i and Σ is the sum over all i, in both cases for i = 0,...,n-1
τᵢ is the length of the interval [Tᵢ,Tᵢ₊₁] in annual units
τ is the period's [T₀,Tₙ] length in annual units
The following features are also supported:
Rate Cutoff
Looking