Research in quantum finance and econophysics, explained from the published literature.
Restated in statistical terms, moving averages and chart patterns ask one question: once we condition on past prices, does the distribution of subsequent returns change? This note sets out the classic studies that tested that question, and the problem of data snooping — where the choice of rules itself shapes the result.
The terms "quantum finance" and "quantum-inspired" are used for three very different kinds of research: computing on quantum computers, classical algorithms inspired by quantum algorithms, and models that describe markets with the mathematics of quantum mechanics. This note sets out what each claims and how each should be judged.
A quantum random walk replaces the coin toss of a classical random walk with a quantum-mechanical operation. Probability amplitudes, not probabilities, are added together, so interference occurs; the distribution spreads in proportion to time and, from a symmetric initial state, takes on a two-peaked shape. This note explains the mechanism and the current state of research applying it to finance.
The hypothesis that share prices follow a random walk goes back to 1900. It holds up well for the direction of price changes and fails for the distribution of their size. This note sets out, from the classic studies, where it holds and where it breaks down.