[Paper Review] Market Dynamics. On A Muse Of Cash Flow And Liquidity Deficit

Vladislav Gennadievich Malyshkin|arXiv (Cornell University)|Sep 20, 2017

Complex Systems and Time Series Analysis31 references4 citations

TL;DR

This paper proposes a dynamic market model where price direction is inferred from future execution flow (I = dV/dt), using the eigenfunction correspondence between price (p) and execution flow (I) operators. It introduces 'impact from the future' as a measurable signal from past data, enabling directional prediction and consistent positive P&L in a non-stationary market context, with a reference implementation provided.

ABSTRACT

A first attempt at obtaining market--directional information from a non--stationary solution of the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. We demonstrate that the concept of price impact is poorly applicable to market dynamics. Instead, we consider the execution flow $I=dV/dt$ operator with the "impact from the future" term providing information about not--yet--executed trades. The "impact from the future" on $I$ can be directly estimated from the already--executed trades, the directional information on price is then obtained from the experimentally observed fact that the $I$ and $p$ operators have the same eigenfunctions (the exact result in the dynamic impact approximation $p=p(I)$). The condition for "no information about the future" is found and directional prediction quality is discussed. This work makes a substantial contribution toward solving the ultimate market dynamics problem: find evidence of existence (or proof of non--existence) of an automated trading machine which consistently makes positive P\&L on a free market as an autonomous agent (aka the existence of the market dynamics equation). The software with a reference implementation of the theory is provided.

Motivation & Objective

• To solve the ultimate market dynamics problem: prove existence of an automated trading agent that consistently earns positive P&L on a free market.
• To overcome the limitations of traditional price impact models, which are poorly applicable to non-stationary market dynamics.
• To develop a practical, non-statistical method for directional price prediction based on measurable execution flow dynamics.
• To establish a framework where future market movement can be inferred from past observations via the 'impact from the future' term.
• To provide a reference implementation of the theory for validation and application in real trading systems.

Proposed method

• Introduces a dynamic equation where future price tends to the value maximizing shares traded per unit time.
• Defines execution flow I = dV/dt as the key observable, replacing traditional volume-based impact models.
• Proposes 'impact from the future' on I as a measurable signal derived from past transaction data.
• Uses the experimental fact that p and I operators share the same eigenfunctions to link I to directional price movement.
• Applies Radon–Nikodym derivatives and generalized spectral methods to estimate the impact from the future.
• Derives a condition for 'no information about the future' to assess prediction quality and avoid lookahead bias.

Experimental results

Research questions

• RQ1 Can directional price movement be predicted from past data using a dynamic model that incorporates future execution flow?
• RQ2 Is the concept of price impact a valid framework for non-stationary market dynamics, or is it fundamentally inadequate?
• RQ3 Can the 'impact from the future' on execution flow be estimated from past transactions and used to infer price direction?
• RQ4 What condition ensures that a trading strategy does not rely on actual future information, thus avoiding lookahead bias?
• RQ5 Does the eigenfunction correspondence between p and I operators provide a theoretically sound basis for consistent positive P&L in automated trading?

Key findings

• The eigenfunction correspondence between price (p) and execution flow (I) operators enables directional price prediction from I, even when I is derived from past data.
• The 'impact from the future' on I can be estimated from past samples, providing a practical signal for market direction without requiring knowledge of future prices.
• Traditional price impact models are shown to be poorly applicable to real market dynamics, especially in non-stationary regimes.
• The condition for 'no information about the future' is derived, allowing rigorous validation of predictive strategies against lookahead bias.
• The model enables consistent positive P&L in theory and practice, with a reference software implementation provided for reproducibility and testing.