Quantum theory of securities price formation in financial markets

TL;DR

This paper introduces a quantum-inspired model for securities price formation that captures complex, fluctuating return distributions and aligns with empirical market data, offering a novel perspective on financial dynamics.

Contribution

It develops a quantum-based theoretical framework for securities prices that does not assume quantum mechanics, explaining non-smooth return distributions and their evolution over time.

Findings

Return distributions exhibit speckle-pattern fluctuations.

Distribution width grows smoothly with time.

Model successfully calibrates to real market data.

Abstract

We develop a theory of securities price formation and dynamics based on quantum approach and without presuming any similarities with quantum mechanics. Disorder introduced by trading environment leads to probability distribution of returns that is not a smooth curve, but a speckle-pattern fluctuating in both price coordinate and time. This means that any given return can at times acquire a substantial probability of occurring while remaining low on average in time. Still, due to local character of order interaction during price formation the distribution width grows smoothly, has a minimum value at small time scale and a square root behavior at large time scale. Examples of calibration to market data, both intraday and daily, are provided.