MICROSTRUCTURAL PRICE FORMATION IN INTERNATIONAL FINANCIAL MARKETS AS A REDUCED NONLINEAR PROCESS

Abstract

The article proves that contemporary international financial markets cannot be adequately described either through the equilibrium price or through the current set of locally observable variables. The purpose of the study is to provide a theoretical and methodological justification for the transition from the equilibrium representation of price to the microstructural mechanism of price formation and to establish the necessity of integral memory for describing the reduced observable state of the market. The relevance of the topic stems from the fact that electronic trading, fragmented liquidity, queue priority, event-based execution, and technological acceleration have transformed modern international financial markets into environments in which price emerges through sequences of submission, execution, cancellation, and liquidity reconfiguration rather than through an abstract and instantaneous coordination mechanism. The research is based on structural-logical analysis, comparative methodology, and conceptual synthesis of works devoted to market microstructure, limit order books, order flow, price impact, and projection-based theories of memory. The article demonstrates that the interaction between aggressive order flow and available liquidity constitutes the causal engine of short-horizon price formation, while the transformation of effort into price result is conditional upon the current state of liquidity, queue structure, cancellations, and execution regime. On this basis, market response is interpreted as nonlinear and state-dependent rather than proportional to the observed impulse. It is further argued that the observable market layer — price, volume, delta, imbalance, and local book configurations — represents only a reduced projection of a wider state space that includes latent liquidity, queue access, and other hidden coordinates. Therefore, the current observable state cannot be treated as a sufficient statistic of subsequent market dynamics. Using the logic of reduced-state projection and the Mori–Zwanzig formalism, the paper substantiates that when hidden coordinates are eliminated from the description, their influence does not disappear but returns in the form of a causal memory term. The practical value of the article lies in providing a rigorous theoretical foundation for the subsequent construction of integral-memory models and the inertial-state metric capable of describing historically loaded market conditions beyond the limits of equilibrium and memoryless interpretations.