Are we using the wrong models? - From a quant website

Excerpted from: Wilmott.com, about Brownian motion and the binomial option pricing model.

PaperCut:

Have you ever traded anything really, really illiquid? I have. It's a real eye-opener on human behavior, markets, and the art form of trading and hedging.

Brownian motion says that there are numerous objects, grayed-out and faded in the background, which buffet a little particle, which winds up having a random walk. We take Brownian motion and confer all kinds of properties to it, and pretend that it's a suitable description of a traded price.

What about those molecules in the background? We say nothing about them. In particular, we don't say anything about their intermolecular potential, which is complicated. I would say their behavior is what needs to be understood.

Not the pollen grain.

In fact, if Brownian motion is a "model" at all, I would call it allegorical at best or an analogy at worst. Consider protein chemistry, where extraordinarily complex intra- and inter- molecular forces cause deformations of the molecular geometry, and resultant transfer of energy from the molecule to its solvent or perhaps another molecule. Now that sounds like a market to me.

farmer:

I disagree that simple, particle-like models are wrong or inadequate. The more complicated model you imagine an individual using, can be achieved by a combination of individuals all using simple models on different subsets of inputs, each trading with a small but distinct portfolio of recurring counterparties. Over time, each individual finds a niche with a small number of subscriptions to certain classifications of events as time series data. One participant's foreground particles are another participant's background particles. A network of such individuals becomes isomorphous with the more complex economic structures which you imagine persist long enough to be modeled. But just as no individual neuron in the brain is aware of any complex thought, nor is any individual trader conscious of the larger model which he and his trading partners are assembled into.

Any time there is a pattern, or repetition of the information which is reflected in propagating waves, complex structures evolve which survive the constant lapping, and which gather up the information in a single representation. There is no reason these structures need to be complete within a single human mind, equity pool, or locus of decision making. Rather, it is natural there will be larger multi-person and multi-corporation structures, which are far more complex than the simple behaviors at each node. The model manifests not in the topology within the node, but within the topology the node finds itself in.