Notional
Key Notional in Interest Fn refers to the notional N on which the interest rate r defined in key Interest Rate acts as it accumulates interest from the reference date d₁ defined in key Accr Start until the date d, where d is the variable input date to the function here.
It is possible to make the notional time-dependent with the help of an amortization scheme supplied as an object of type Amortization through the key Amortization in combination with a schedule of amortization dates that by default equals the reference dates d₁, d₂ , ... , dᵤ defined in Accr Start, but can be also defined independently of the reference dates by using the optional key Amort Schedule
Either way, a series of n dates D₁, D₂ , ... , Dₙ is generated on which the effective notionals N₁, N₂ , ... , Nₙ apply, with the correspondence as below:
D₁ ↔ N₁ , D₂ ↔ N₂ , ... , Dₙ ↔ Nₙ
For example, if d = D₃, the interest is the amount accrued from d΄ to D₃, where d΄ is the reference date closest to and strictly earlier than D₃ while the notional is assumed to equal N₂
Only if d > D₃, the applicable notional will cease to equal N₂
Amortization payments can also become part of the function's output so that the function returns the total payment due on the given date d composed by the sum of the accrued interest and the amortized notional.
This can be specified through the key Change Is Paid in the already mentioned object of type Amortization supplied through the key Amortization
For example, if d = D₃ and Change Is Paid = true, the function's output will equal the sum of the interest accrued from d΄ to D₃ and the difference N₃ - N₂
Note, the amount N₃ - N₂ is added to the function's output only if d equals one of the amortization dates D₁, D₂ , ... , Dₙ
In the case of several reference dates with or without amortization, the applicable interest rate and set of conventions for each input date d is selected as described respectively at Interest Rate and Spec