# The Action Principle in Market Mechanics

## TL;DR

This paper proposes a physics-inspired model of asset prices, treating them as harmonic oscillators constrained by an action principle, enabling predictions of extreme movements and future displacements based on historical data.

## Contribution

It introduces a novel approach applying physical laws and the principle of stationary action to model and forecast asset price dynamics.

## Key findings

- Model accurately predicts constraints on extreme price movements.
- The harmonic oscillator analogy fits observed price dynamics.
- The approach provides probabilistic forecasts of future price displacements.

## Abstract

This paper explores the possibility that asset prices, especially those traded in large volume on public exchanges, might comply with specific physical laws of motion and probability. The paper first examines the basic dynamics of asset price displacement and finds one can model this dynamic as a harmonic oscillator at local "slices" of elapsed time. Based on this finding, the paper theorizes that price displacements are constrained, meaning they have extreme values beyond which they cannot go when measured over a large number of sequential periods. By assuming price displacements are also subject to the principle of stationary action, the paper explores a method for measuring specific probabilities of future price displacements based on prior historical data. Testing this theory with two prevalent stock indices suggests it can make accurate forecasts as to constraints on extreme price movements during market "crashes" and probabilities of specific price displacements at other times.