Trade group

An operation. Every other trade set exists because something in the business names it: a book, a netting agreement, a structure. A trade group exists because a process ran.

A process is a kind of operation, such as a funding roll or a compression. A run is one instance of it, with an identity, a time and an actor. A trade group is a trade set created for one run. Membership is the rows of that group, each naming a trade and the role it played.

The group carries the foreign key to the run, and the run carries the foreign key to the process. That key is not bookkeeping. It is what makes the inputs, the outputs and the undo reachable from one another, and it is what determines the roles.

The foreign key to the run fixes the vocabulary. The role column's allowed values belong to the process, not to a global list, so a batch's members carry no role and a funding run's groups have to be told apart.

A batch is the case that shows the rule. It selects trades and values them, and it says nothing about what any of them is. It reads and writes no trade, so it needs one group and has no second group to tell apart, and its members carry no role.

The two group roles say what the run did with the set. input is what the run read and output is what it wrote. They are a property of the run's reading and writing rather than a partition of the trades, so a trade can be in both.

Compression is the case that shows it. A negotiated run terminates some trades in full, reduces others, and creates replacements. A terminated trade is in the input only, a reduced trade is in both because the same trade survives with a smaller notional, and a replacement is in the output only. The member's role says which, so the role and the groups a trade belongs to have to agree. Trade compression gives the mechanics.

Compression does not always cancel the population out. It preserves net risk, so where the population's net exposure is not zero the output carries it, as surviving trades or as replacements. Even the firm's own tear-up process books a deal for each trade it removes. Netting is the opposite case: it refuses a residual, where compression absorbs one.

A run of a process that writes no trade still produces a group, because the set it read is the thing a repeat has to reconstruct.

What a run promises follows from what a run of that process does, so the process declares it.

A funding roll creates and ends trades. Its run has to create them together or not at all, and it has to be undoable as a whole, and the undo has to leave profit and loss where it was. A batch changes no trade, so there is nothing to create together, nothing to undo, and no economic effect to reverse.

Putting either obligation on the group would give a batch a funding roll's duties. Putting them on the process gives each run the promises its own kind of operation can keep.

In mathematics a group is a set together with a binary operation that satisfies closure, associativity, and the existence of an identity and inverses. The weakest rung of the same idea is a magma, which is a set with a binary operation and no axioms at all. Both take the operation to be closed on the set and to combine two members into one.

A process does not do that. It reads a trade set and writes a trade set, which is a function from the collection of trade sets to itself. The mathematical reading is a transition rather than an operation, and the structure is a transition system: states, and the moves between them. The word "group" is right for the set-plus-operation idea and wrong for the algebra those axioms describe.

The clearest evidence that the axioms do not hold is already in the analysis notes on netting: netting is not allowed if there is a residual. A residual is the operation failing to close.

• A group is a table with a key and a foreign key to its run.
• Membership is a table keyed by the group and the trade, with the role column whose values the process fixes.
• A process declares the group-level roles and the trade-level roles a run of it may use.
• Undo belongs to the run, so it reverses a run rather than deleting a group.