Term Rate


Term Rate is a
direct subtype of Interest Rate with functions Term Rate Functions, direct subtypes Term Rate subtypes, keys Term Rate keys and example object TermRt that represents the notion of an interest rate r that is associated with a simple lending (or borrowing) of a currency amount over a single time period Δ referred as its "spanning period".
Δ is specified as an object of type
Step, without its start and end dates being defined.
If Δ is left undefined, the corresponding spanning period is implied by the context.
This is the case with the
direct subtype OI Term Rate where the spanning period is often set equal to the applicable period of the floating leg of the OIS where the OI Term Rate applies.
The precise corresponding spanning time interval [T₁,T₂] is context dependent.
For example, a Δ of 6 months can be used to describe a 6-month rate that accrues from T₁ = 1 Mar 2020 to T₂ 1 Sep 2020, but also a 6-month rate that accrues from T₁ = 20 Apr 2024 to T₂ = 20 Oct 2024.

The Term Rate also contains a daycount convention so that the time legth t in annual units of the the referenced time interval [T₁,T₂] can be calculated.
Then the interest amount on a notional of one currency unit accrued over the period Δ is given by a simple formula that depends on a specified
Frequency and Compounding
In the special case when the Frequency is
None and the Compounding is Simple, the accrued amount A is given by the formula:
A = rt

In a given pricing context, the numerical value of r depends on the prevailing market conditions and the applicable spanning time interval [T₁,T₂] and becomes known (i.e. fixed) at some time T₀ such that T₀ < T₁
T₀ is known as the rate's "fixing date" or "reset date".
T₁ is known as the rate's "value date".
The time period from T₀ to T₁ is known as the rate's "settlement period" and specified through the key
Settlement

The known r - for example r = 4% - is often assumed to accrue over some interval [Tᵃ₁,Tᵃ₂], referred as "accrual interval", of which the times Tᵃ₁ , Tᵃ₂ may differ from the spanning interval times T₁ , T₂

The interval [Tᵃ₁,Tᵃ₂] is usually the starting point for finding out the the fixing date T₀
Then, a date of that interval is selected as the reference date Tᴿ, based on which the fixing date T₀ is calculated.
Usually, Tᴿ is chosen to be the accrual interval's start date Tᵃ₁ (vanilla case), or end date Tᵃ₂ (in arrears case).

The number n of business days from T₀ to Tᴿ is known as the rate's "fixing days" and normally equals the days specified in the settlement period.
It is nevertheless possible to set n to any custom value - even negative - by means of the key
Fixing Days

The important characteristic that distinguishes a Term Rate from other rate types - such as the
Swap Rate or the Short Rate - is the fact that the spanning period Δ is a single, finite time interval, which can be associated with two varying distinct dates T₁ and T₂ with T₁ < T₂