Adam Smith noted man's "propensity to truck, barter, and exchange one thing for another" in The Wealth of Nations. It is worth quoting what he had to say just after this:

Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog. Nobody ever saw one animal by its gestures and natural cries signify to another, this is mine, that yours; I am willing to give this for that. When an animal wants to obtain something either of a man or of another animal, it has no other means of persuasion but to gain the favour of those whose service it requires. A puppy fawns upon its dam, and a spaniel endeavours by a thousand attractions to engage the attention of its master who is at dinner, when it wants to be fed by him. Man sometimes uses the same arts with his brethren, and when he has no other means of engaging them to act according to his inclinations, endeavours by every servile and fawning attention to obtain their good will. He has not time, however, to do this upon every occasion. In civilised society he stands at all times in need of the cooperation and assistance of great multitudes, while his whole life is scarce sufficient to gain the friendship of a few persons. In almost every other race of animals each individual, when it is grown up to maturity, is entirely independent, and in its natural state has occasion for the assistance of no other living creature. But man has almost constant occasion for the help of his brethren, and it is in vain for him to expect it from their benevolence only. He will be more likely to prevail if he can interest their self-love in his favour, and show them that it is for their own advantage to do for him what he requires of them. Whoever offers to another a bargain of any kind, proposes to do this. Give me that which I want, and you shall have this which you want, is the meaning of every such offer; and it is in this manner that we obtain from one another the far greater part of those good offices which we stand in need of.

The italics are not in the original text.

Financial transactions occur between two counterparties - a buyer and a seller. The buyer decides the amount of a given instrument to acquire in exchange for another, and chooses a seller offering an an acceptable price. There is an inherent asymmetry in every transaction.

Every transaction occurs at the time the buyer decides to exchange something with a seller. The buyer receives a quantity of something in exchange for a quantity of another thing. This can be described in mathematical notation by χ = (t; a, i, c; a', i', c') - at time t buyer c acquires amount a of instrument i in exchange for amount a' of instrument i' from seller c'.

As with all mathematical models, this simplifies what happens in the real world. In reality, transactions require quite a bit of plumbing to make this abstraction useful. Someone has to set up the mechanisms that enable these transactions whether over-the-counter or exchange traded.  Collateral agreements and margin requirements are completely ignored by this model, as are limit orders and other types of transactions that do not occur on the spot. This is just a first cut at extending the mathematical theory to not assume perfect liquidity and that all counterparties can participate at the same price.

Bean Counting

Last edited Dec 2, 2011 at 12:17 AM by keithalewis, version 19