Slope Step Up


Key Slope Step Up in
Scheduled Linear Fn refers to a 1D-array of m objects S₁ , S₂ , ... , Sₘ of type Step Up Rule that are used to generate the parameter Slope of each Linear Fn function that applies at each scheduled date.
Concretely, let d₁ , d₂ , ... , dᵣ be the sequence of dates implied by the entry in key
Schedule
On the first date d₁, the applicable function is already given and equals the base function ƒ₁ defined in key
Fn
Let ƒ₁ be characterized by the parameters
Slope = m₁, m₂, ..., mᵤ and Intercept = c
On the second date d₂, the applicable function is generated by the new parameters
Slope = m'₁, m'₂, ..., m'ᵤ and Intercept = c'
The new parameters m'₁, m'₂, ..., m'ᵤ are constructed by applying the
Step Up Rule objects S₁ , S₂ , ... , Sₘ defined in the key here on the base parameters m₁, m₂, ..., mᵤ
The new parameter c' is constructed similarly, but by applying the
Step Up Rule object defined in the key Intercept Step Up
Comcretely, S₁ is applied on m₁ and produces the m'₁, then S₂ is applied on m₂ and produces the m'₂ and so on.
If m < u, the sequence S₁ , S₂ , ... , Sₘ is extended based on its last elements, i.e. new elements Sₘ₊₁ , Sₘ₊₂ , ... , Sᵤ₋₁ , Sᵤ are added such that all are equal to Sₘ