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on Market Microstructure |
| By: | Rama Cont (University of Oxford); Pierre Degond (IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique); Xuan Lifan (Imperial College London) |
| Abstract: | We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a deterministic 'mass transport' operator acting on distributions of buy and sell orders. At the mathematical level, this corresponds to a natural decomposition of the infinitesimal generator describing the evolution of the limit order book into two operators: the generator of the order flow and the clearing operator. Our model provides a flexible framework for modelling and simulating order book dynamics and studying various scaling limits of discrete order book models. We show that our framework includes previous models as special cases and yields insights into the interplay between order flow and price dynamics. |
| Keywords: | Limit order book, stochastic model, quantitative finance, market microstructure, measurevalued process |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-03968767 |
| By: | Youssef Ouazzani Chahdi; Mathieu Rosenbaum; Gr\'egoire Szymanski |
| Abstract: | While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by developing a microstructure model connecting liquidity dynamics and price moves. A key innovation of our approach is to replace the traditional assumption of constant information content for each trade by a function that depends on the available volume in the limit order book. Within this framework, we explore scaling limits and analyze the market impact of passive metaorders. Additionally, we derive useful approximations for the shape of market impact curves, leading to closed-form formulas that can be easily applied in practice. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.07461 |
| By: | Mohammed Salek (CentraleSupélec, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay); Damien Challet (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay); Ioane Muni Toke (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay) |
| Abstract: | Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in turn, results in a reduced price impact and decreased volatility of the indicative price. In this study, we adapt the latent/revealed order book framework to the specifics of equity auctions. We provide precise measurements of the model parameters, including order submissions, cancellations, and diffusion rates. Our setup allows us to describe the full dynamics of the average order book during closing auctions in Euronext Paris. These findings support the relevance of the latent liquidity framework in describing limit order book dynamics. Lastly, we analyze the factors contributing to a sub-diffusive indicative price and demonstrate the absence of indicative price predictability. |
| Keywords: | Market microstructure, Continuous models, Statistical analysis, Equity auctions |
| Date: | 2024–01–12 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04391810 |
| By: | Yun Chen-Shue; Yukun Li; Jiongmin Yong |
| Abstract: | We introduce a model for limit order book of a certain security with two main features: First, both the limit orders and market orders for the given asset are allowed to appear and interact with each other. Second, the high frequency trading activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model has been derived as a stochastic partial differential equation (SPDE, for short), under certain intuitive identifications. Its diffusion coefficient is determined by a Volterra integral equation driven by a Hawkes process, whose Hurst exponent is less than 1/2 (so that the relevant process is negatively correlated). As a result, the volatility path of the SPDE is rougher than that driven by a (standard) Brownian motion. The well-posedness follows from a result in literature. Hence, a foundation is laid down for further studies in this direction. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.16850 |
| By: | Ritwika Chattopadhyay; Abhishek Malichkar; Zhixuan Ren; Xinyue Zhang |
| Abstract: | This paper addresses the challenges faced in large-volume trading, where executing substantial orders can result in significant market impact and slippage. To mitigate these effects, this study proposes a volatility-volume-based order slicing strategy that leverages Exponential Weighted Moving Average and Markov Chain Monte Carlo simulations. These methods are used to dynamically estimate future trading volumes and price ranges, enabling traders to adapt their strategies by segmenting order execution sizes based on these predictions. Results show that the proposed approach improves trade execution efficiency, reduces market impact, and offers a more adaptive solution for volatile market conditions. The findings have practical implications for large-volume trading, providing a foundation for further research into adaptive execution strategies. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.12482 |