Accumulator Accr Claim
Accumulator Accr Claim is a direct subtype of Contingent Claim
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with functions Accumulator Accr Claim Functions, keys Accumulator Accr Claim keys and example object AccumAccrClaim
TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Accumulator Accr Claim
This type represents the periodic - typically daily - accumulation of shares in the context of an accumulator (decumulator) contract associated with the related Structured Product
At each relevant time t, the number of shares accrued at each relevant date is added in a special non-cash accumulation account.
Formally, it can be regarded as a non-cash Payoff conditional on the occurrence of the associated event at each applicable observation timet, which event may be referred here as the accumulation accrual event
The claim must always coexist with 3 other claims of type Accumulator Pmt Claim, Accumulator Settled Total Claim and Accumulator Days Total Claim
The non-cash Payoff at each applicable observation time t does not represent cash, but rather the accumulated number of shares that are stored in the special non-cash accumulation account.
It eqwuals the number of shares that has been accumulated since the most recent time prior to t when these shares were bought or sold on behalf of the investor in the context of a related Structured Product
At each observation time t, a fixed number of shares is added to the so far accumulated total number of shares.
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 Accumulator Accr Claim, these are as below:
Condition
This claim's condition is trivial, in the sense it is assumed to be satisfied at each observation time
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 is set to RealBoolTransf, which is a predicate function that always returns TRUE
ON Payoff
This concerns the non-cash Payoff amount ON amt representing the accumulated number of shares associated with the condition being satisfied at any applicable observation time t
Since the condition is always satisfied, ON amt is always calculated at each applicable t
The amount ON amt is calculated by the function ƒON associated with the key On Pmt Fn of its direct container typeContingent Claim
Note, the amount ON amt is not paid out to the investor, but simply stored in the special non-cash account designated with the text label defined in Account Name
The function ƒON expects as input the 3 arguments: (t, a, s), where
t = the observation time (actually a date)
a = the accumulated shares already existing in the special non-cash account at time t
s = the share price of the laggard underlying observed at time t
The formula is:
ƒON(t , a , s) = (L-1) N b + N if t is a settlement day
ƒON(t , a , s) = a + (L-1) N b + N if t is any other non-settlement day
Above, b is a Boolean in binary form: 1 if s ∊ leverage regime, 0 otherwise. In effect it is the indicator function wrt the leverage regime.
Technically, the function ƒON is represented by an object of type Timed Comp Real Fn, which implements the composition h₂ ⸰ h₁ of two functions:
(h₂ ⸰ h₁)(x) = h₂( h₁(x) )
The function h₁ is an object of type Array Fn with formula:
h₁(a , s) = (a , b)
The second function h₂ is an object of type Scheduled Linear Fn with formula:
h₂(t , a , s) = (L-1) N b + N if t is a settlement day
h₂(t , a , s) = a + (L-1) N b + N if t is any other non-settlement day
OFF Payoff
This claim has no payoff associated with the condition not being satisfied.