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The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…

General Finance · Quantitative Finance 2019-02-28 J. L. Subias

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders-large orders that are split into smaller…

Trading and Market Microstructure · Quantitative Finance 2022-05-17 Emilio Said , Ahmed Bel Hadj Ayed , Damien Thillou , Jean-Jacques Rabeyrin , Frédéric Abergel

Standard models of asset price dynamics, such as geometric Brownian motion (see, for example, Osborne, 1959, Samuelson, 2016), do not formally incorporate investor inertia. This paper presents a two-stage framework for modelling this…

Theoretical Economics · Economics 2025-11-27 Diego da Silva Santos , Luiz Gustavo Bastos Pinho

The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all…

Trading and Market Microstructure · Quantitative Finance 2018-01-17 Felix Patzelt , Jean-Philippe Bouchaud

Financial markets exhibit an apparent paradox: while directional price movements remain largely unpredictable--consistent with weak-form efficiency--the magnitude of price changes displays systematic structure. Here we demonstrate that…

Trading and Market Microstructure · Quantitative Finance 2025-12-19 Mainak Singha

We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a…

Statistical Finance · Quantitative Finance 2026-02-03 Johannes Muhle-Karbe , Youssef Ouazzani Chahdi , Mathieu Rosenbaum , Grégoire Szymanski

In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…

Pricing of Securities · Quantitative Finance 2008-12-23 Damiano Brigo , Fabio Mercurio

We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic…

Trading and Market Microstructure · Quantitative Finance 2015-05-20 Weibing Huang , Mathieu Rosenbaum

Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged…

Other Condensed Matter · Physics 2008-12-02 J. -P. Bouchaud , J. Kockelkoren , M. Potters

It is a challenging task to identify the best possible models based on given empirical data of observed time series. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big…

Statistical Finance · Quantitative Finance 2021-11-05 Vygintas Gontis

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic…

Trading and Market Microstructure · Quantitative Finance 2018-04-02 Kiyoshi Kanazawa , Takumi Sueshige , Hideki Takayasu , Misako Takayasu

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all…

Trading and Market Microstructure · Quantitative Finance 2015-06-18 Yoshihiro Yura , Hideki Takayasu , Didier Sornette , Misako Takayasu

Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context…

adap-org · Physics 2015-06-30 J. Doyne Farmer

We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…

Statistical Mechanics · Physics 2013-05-29 Marcus G. Daniels , J. Doyne Farmer , Laszlo Gillemot , Giulia Iori , Eric Smith

We develop a new market-making model, from the ground up, which is tailored towards high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure. Our flexible…

Trading and Market Microstructure · Quantitative Finance 2020-01-31 Baron Law , Frederi Viens

This note explores the consequences of nonlinear price impact functions on price dynamics within the chartist-fundamentalist framework. Price impact functions may be nonlinear with respect to trading volume. As indicated by recent empirical…

Other Condensed Matter · Physics 2009-11-10 Frank Westerhoff

We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and…

Trading and Market Microstructure · Quantitative Finance 2014-12-09 Elia Zarinelli , Michele Treccani , J. Doyne Farmer , Fabrizio Lillo

This paper is devoted to the important yet unexplored subject of crowding effects on market impact, that we call "co-impact". Our analysis is based on a large database of metaorders by institutional investors in the U.S. equity market. We…

Trading and Market Microstructure · Quantitative Finance 2018-07-10 Frédéric Bucci , Iacopo Mastromatteo , Zoltán Eisler , Fabrizio Lillo , Jean-Philippe Bouchaud , Charles-Albert Lehalle

This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price…

Probability · Mathematics 2015-05-05 Vladimir Vovk

We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…

Pricing of Securities · Quantitative Finance 2025-07-01 Nader Karimi