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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Minimal price series models - article

The New Scientist had a story recently about a Santa Fe Institute stock market study that started from the assumption of zero intelligence on the part of traders - the polar opposite of typical econ idealizations of rational traders with perfect information. Essentially they used a random model. The article can be found here -

http://www.newscientist.com/article.ns?id=dn6948

The lead author on the original paper is J. Doyne Farmer.

It is a reasonable thing to try, but the "very closely" claim doesn't quite follow from their actual results. While random orders did produce realistic bid-ask spreads - which largely amounts to saying bid-ask spreads basically reflect a momentary normal distribution of valuations around the current market price - their data only explained about 3/4 of price diffusion over a length of time of a little under two years.

Which amounts to saying a random walk is a decent first approximation to any price series but the real market isn't quite a random walk. The remaining 1/4 of price diffusion is the trend or signal, the rest is well approximated as random walk style noise.

What is nice about it is simply the realistic idea of disaggregating "buy" and "sell" into "buy at or below" and "sell at or above" valuations, and seeing how distributions of those interact to produce trades.

What would be a nice addition would be to disaggregate trader valuation models (or return expectations), into a small set of simple assumptions. Have different starting subsets use different models. As the price moves, it would effect the buy and sell limit order willingness of different subsets of traders differently.

It is much more plausible that traders use a variety of simple models that each differ only marginally from "zero intelligence", than that all traders use the same model that encapsulates perfect intelligence. It seems to me it is also more likely to produce outcomes that look "close to but not quite" random walk or diffusion like. Getting the "not quite" part right is what neither extreme assumption - perfect information or no information - can adequately account for.

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