Wolfram Computation Meets Knowledge

Wolfram Summer School


Philip Maymin

Summer School

Class of 2007


I am a PhD candidate in finance at the University of Chicago and a founder and manager of a hedge fund in Greenwich, CT. I’m also a Justice of the Peace, a weekly columnist for the Fairfield County Weekly, a policy scholar for the Yankee Institute, in which role I have written for the Connecticut Post, Hartford Business Journal, and Waterbury Republican-American, among others, and a former Libertarian candidate for the U.S. House of Representatives from Connecticut’s fourth Congressional district. I’m also a former sports journalist and quantitative basketball analyst. I got a Master’s in Applied Math and a Bachelor’s in Computer Science from Harvard after I graduated from Phillips Academy. I have also completed two years of Northwestern California University School of Law’s online J.D. program and passed the California Baby Bar exam.

Project: Minimal Models of the Complexity of Financial Security Prices

What’s the simplest rule to model the complexity and randomness of financial markets? Security prices have complex behavior in the time series and cross section of prices, returns, volume, and liquidity. It’s easy to mimic security prices by introducing randomness, either externally like a random walk or internally through large structures such as cellular automata involving trade between many investors, but what are the minimal models that generate complexity?

One Trader

I find that a single investor trading in a single security can generate complex price behavior all by himself. He makes trading decisions by looking back at the signs of the price change over the past few days. Because he is the representative investor, the price adjusts with his decisions.

The Simplest Rule with Complex Behavior

Rule 54 is the only interesting 2-state buy/sell rule with lookbacks up to 15. With fixed lookbacks, the price series will always cycle, but rule 54 often achieves near maximal cycle lengths, which can be quite long. For example, a 15-business-day lookback will cycle in about 130 years.

More Complicated Rules

Surprisingly, allowing an infinite lookback window, so that the trader looks back over each price change in the security’s history back to its very first day, removes complexity. There are no rules with either two or three internal states that produce interesting behavior: all cycle very quickly. Allowing the lookback window to grow on a log scale, so that the trader looks back one more day before he is likely to cycle, does produce complex behavior arbitrarily far, though sometimes with long periods of high predictability interspersed.

Multiple Traders

When several rules trade in the same security, we can also generate the trading volume and measures of liquidity. Sometimes complex rules trade and remove complexity and sometimes simple rules trade and create complexity. Liquidity falls, even though volume is constant, before a crash.

Project-Related Demonstrations

Trader Dynamics in Minimal Models of Financial Complexity

View demonstration of Wolfram Demonstrations Project

The Minimal Model of the Complexity of Financial Security Prices

View demonstration of Wolfram Demonstrations Project

Exploring Minimal Models of the Complexity of Security Prices

View demonstration of Wolfram Demonstrations Project

Minimal Model of Simulating Prices of Financial Securities Using an Iterated Finite Automaton

View demonstration of Wolfram Demonstrations Project

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 3892055

My favorite 3-color outer totalistic cellular automaton is rule 3892055.

Because outer totalistic CAs are symmetrical around the middle when starting with a single black cell, I started with the simplest possible non-symmetrical two-color initial conditions: {{1,0,1,1},0}. Then I did a random search, filtering by complexity.

Rule 3892055 starts off slow and gets more and more complex with time. The attached notebook and the pictures below shows its evolution for the first 7,500 steps, the 5,000 steps after that, and the 5,000 steps after that, each snapshot zoomed in to the most interesting part.