KI Claim
KI Claim is a direct subtype of Contingent Claim
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE KI Claim
This type represents the knock-in payment associated with the related Structured Product
Formally, it can be regarded as a payment conditional on the occurrence of the associated event at each applicable observation timet, which event may be referred here as the knock-in event
As described in Contingent Claim, the three main ingredients of every Contingent Claim are the condition the ON payoff and the OFF payoff
In the case of a KI Claim, these are as below:
Condition
As described in Contingent Claim, technically every condition is represented by a predicate function 𝘨 associated with the key Trigger Fn of its container typeContingent Claim
Here 𝘨 expects as input the performances (also known as growth factors) P₁ , P₂ , ... , Pᵤ of the u underlyings U₁ , U₂ , ... , Uᵤ, as observed at the observation time t
The performances are defined as follows:
P₁ , P₂ , ... , Pᵤ = x₁/x⁰₁ , x₂/x⁰₂ , ... , xᵤ/x⁰ᵤ
where
x₁ , x₂ , ... , xᵤ are the market prices of the underlyings U₁ , U₂ , ... , Uᵤ observed at t
x⁰₁ , x⁰₂ , ... , x⁰ᵤ are fixed reference prices of the underlyings that are part of the note's definition.
The concept of a trigger region is also required in formulating the predicate function 𝘨
In its simplest form, a trigger region is a single interval in the axis of real numbers, such as the interval (1 , +∞)
The predicate function 𝘨 can be one of two types:
1) At least one of P₁ , P₂ , ... , Pᵤ is within the trigger region
2) All of P₁ , P₂ , ... , Pᵤ are within the trigger region
Here 𝘨 is set to Scheduled Number Is Inside Fn, which is a predicate function that returns TRUE if the referenced performances are within the trigger region
ON Payoff
This concerns the payoff amount ON amt associated with the condition being satisfied at any applicable observation time t
The amount ON amt is calculated by the function ƒON associated with the key On Pmt Fn of its direct container typeContingent Claim
The function ƒON expects as input the u + 1 arguments (t, x₁ , x₂ , ... , xᵤ)
The formula is:
ƒON(t, x₁ , x₂ , ... , xᵤ) = (hₚ ⸰ hₘ)(t, x₁ , x₂ , ... , xᵤ)
(hₚ ⸰ hₘ) is the composition of the follwoing functions:
hₘ returns the minimum or maximum p of the performances P₁ , P₂ , ... , Pᵤ
hₚ receives as input the time t and the output performance p from hₘ and returns the final payoff depending on where p lies on the real axis.
The applicable formula is determined by finding out which part of the payoff structure defined in key Triggered Payoff applies on the particular value of p
OFF Payoff
This concerns the payoff amount OFF amt associated with the condition being satisfied at any applicable observation time t
The amount OFF amt is calculated by the function ƒOFF associated with the key Off Pmt Fn of its direct container typeContingent Claim
The function ƒOFF is similar to ƒON with the only difference being that the applicable formula is determined by the payoff structure defined in key Non Triggered Payoff