Alive On Payoffs
Key Alive On Payoffs in Payoff Policy refers to an optional set of ON payoff valuations - represented as an object of type KeySet - that are meant to stay "alive" (i.e. the payoffs remain due for valuation and settlement) after an event associated with any specific claim is triggered provided the claims to such payoffs have been established but their corresponding payoff amounts have not been valuated prior to that event.
Note, the ON payoffs are those associated with the key On Pmt Fn of the various Contingent Claim objects.
In effect, the entry here introduces an exception to the default rule applying to all policies whereby the occurrence of any event causes the deactivation of all subsequent claims and all subsequent payoff valuations.
In more formal terms, it defines an optional mapping 𝘨ᴬᴾ (AP for Alive Payoffs) that establishes an association between certain selected Contingent Claim objects to corresponding sets of Contingent Claim objects, which association affects the payoff payments of the claims in those sets as described below.
So, formally 𝘨ᴬᴾ acts on any such selected Contingent Claim object C as follows:
𝘨ᴬᴾ: C → { C₁ , C₂ , ... , Cᵣ }
where r is a positive integer.
and C₁ , C₂ , ... , Cᵣ are all available Contingent Claim objects.
Before explaining the meaning of this association, a fact must be stated regarding the default impact that any trigger event has on all other trigger events, past, present and future.
By default, when a trigger event takes place, all future claims will cease to exist and also any payoff commitments that were perhaps established by previous trigger events are deemed void and need not be honored.
For example, a typical barrier knock-out event exemplifies this generic default rule since only the payoff (i.e. the barrier rebate) associated with this event is paid and all other claims simply disappear, including the claim associated with future knock-out events at the same barrier.
The mapping defined here allows to override this default rule with respect to events triggered by certain selected claims.
Concretely, for any claim C in the mapping defined here, the following holds:
If during a simulation run at some time T an event E takes place, whereby the claim C is triggered , then if any of the claims in the set { C₁ , C₂ , ... , Cᵣ } had been triggered prior to the event E establishing corresponding ON payoff commitments to be honored at or after T, such payoff commitments will be unaffected by the event E, i.e. will stay alive.
Note, the ON payoff commitments are those associated with the key On Pmt Fn of the various Contingent Claim objects.
Below are the technical details on how the Alive On Payoffs mapping is implemented on the spreadsheet.
a) The key Alive On Payoffs expects an object of type KeySet and works as follows:
The names used for the Keys part of the KeySet object serve to identify the special claims C discussed above by means of the unique ID each claim bears through its key Claim ID.
It is therefore imperative that the chosen key names cannot be arbitrary, as they should match the IDs of the objects defined through the key Contingent Claims.
b) The Value corresponding to each key is expected to be a 1D-array of text labels that - similarly as with the keys - are interpreted as claim IDs and thus identify the associated Contingent Claim objects.
For example:
Let a key be PARTIAL-KO= and let its associated value be an array consisting of the two labels KI-BARRIER and DEFERRED-COUPON.
The meaning of this assignment is as follows:
First of all, the assignment becomes relevant only if:
1) The trigger of the Contingent Claim object whose Claim ID equals PARTIAL-KO fires up, i.e. if that object's embedded Trigger Fn valuates to TRUE during the simulation.
and
2) By the time the afore mentioned event occurrs, other prior events have already occurred that gave rise to payoffs destined to be paid out in the future of that event
If both of the above conditions hold, the assignment decides which - if any - of the already claimed but still pending payoffs must be fulfilled at their stipulated payout time during that simulation.
For example, assume the PARTIAL-KO trigger fires up at some time during a simulation run, while prior to that time only the DEFERRED-COUPON trigger hapenned to fire a few times.
Furthermore assume that a few of the past DEFERRED-COUPON trigger fire ups had led to payoffs with payment dates lying after the activation of the PARTIAL-KO event.
Then this assignment stipulates that all such payoffs must be honored at their expected payment times.
Note it is not required that all Contingent Claim objects are represented through the keys here.
In fact, it is sensible to not include a Contingent Claim that acts as a typical knock-out, since in the case of a knock-out event no further payments are usually made.
Alternatively, the key associated with a knock-out Contingent Claim may still be present, but with an empty associated array of labels.