The Minimal Model of Financial Complexity

TL;DR

This paper introduces the simplest deterministic model of financial markets that generates realistic, complex price paths with features like fat tails and crashes, without parameter fitting.

Contribution

It presents the minimal deterministic model of financial complexity, demonstrating how simple rules can produce realistic market behaviors and generalize to more complex dynamics.

Findings

Generates realistic price paths with fat tails and crashes

Produces more complex dynamics than a random walk

Does not require parameter fitting

Abstract

A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy. This simple, unique, and robust model is the smallest possible deterministic model of financial complexity, and its generalization leads to complex variety. Compared to a random walk, the minimal model generates time series with fatter tails and more frequent crashes, thus more closely matching the real world. It does all this without any parameter fitting.