Market Microstructure

Looking into informal currency markets as Limit Order Books: impact of market makers ArXiv ID: 2503.03858 “View on arXiv” Authors: Unknown Abstract This study pioneers the application of the market microstructure framework to an informal financial market. By scraping data from websites and social media about the Cuban informal currency market, we model the dynamics of bid/ask intentions using a Limit Order Book (LOB). This approach enables us to study key characteristics such as liquidity, stability and volume profiles. We continue exploiting the Avellaneda-Stoikov model to explore the impact of introducing a Market Maker (MM) into this informal setting, assessing its influence on the market structure and the bid/ask dynamics. We show that the Market Maker improves the quality of the market. Beyond their academic significance, we believe that our findings are relevant for policymakers seeking to intervene informal markets with limited resources. ...

To Hedge or Not to Hedge: Optimal Strategies for Stochastic Trade Flow Management ArXiv ID: 2503.02496 “View on arXiv” Authors: Unknown Abstract This paper addresses the trade-off between internalisation and externalisation in the management of stochastic trade flows. We consider agents who must absorb flows and manage risk by deciding whether to warehouse it or hedge in the market, thereby incurring transaction costs and market impact. Unlike market makers, these agents cannot skew their quotes to attract offsetting flows and deter risk-increasing ones, leading to a fundamentally different problem. Within the Almgren-Chriss framework, we derive almost-closed-form solutions in the case of quadratic execution costs, while more general cases require numerical methods. In particular, we discuss the challenges posed by artificial boundary conditions when using classical grid-based numerical PDE techniques and propose reinforcement learning methods as an alternative. ...

A New Traders’ Game? – Empirical Analysis of Response Functions in a Historical Perspective ArXiv ID: 2503.01629 “View on arXiv” Authors: Unknown Abstract Traders on financial markets generate non-Markovian effects in various ways, particularly through their competition with one another which can be interpreted as a game between different (types of) traders. To quantify the market mechanisms, we empirically analyze self-response functions for pairs of different stocks and the corresponding trade sign correlators. While the non-Markovian dynamics in the self-responses is liquidity-driven, it is expectation-driven in the cross-responses which is related to the emergence of correlations. We empirically study the non-stationarity of these responses over time. In our previous data analysis, we only investigated the crisis year 2008. We now considerably extend this by also analyzing the years 2007, 2014 and 2021. To improve statistics, we also work out averaged response functions for the different years. We find significant variations over time revealing changes in the traders’ game. ...

Ornstein-Uhlenbeck Process for Horse Race Betting: A Micro-Macro Analysis of Herding and Informed Bettors ArXiv ID: 2503.16470 “View on arXiv” Authors: Unknown Abstract We model the time evolution of single win odds in Japanese horse racing as a stochastic process, deriving an Ornstein–Uhlenbeck process by analyzing the probability dynamics of vote shares and the empirical time series of odds movements. Our framework incorporates two types of bettors: herders, who adjust their bets based on current odds, and fundamentalists, who wager based on a horse’s true winning probability. Using data from 3450 Japan Racing Association races in 2008, we identify a microscopic probability rule governing individual bets and a mean-reverting macroscopic pattern in odds convergence. This structure parallels financial markets, where traders’ decisions are influenced by market fluctuations, and the interplay between herding and fundamentalist strategies shapes price dynamics. These results highlight the broader applicability of our approach to non-equilibrium financial and betting markets, where mean-reverting dynamics emerge from simple behavioral interactions. ...

The Market Maker’s Dilemma: Navigating the Fill Probability vs. Post-Fill Returns Trade-Off ArXiv ID: 2502.18625 “View on arXiv” Authors: Unknown Abstract Using data from a live trading experiment on the Binance Bitcoin perpetual, we examine the effects of (i) basic order book mechanics and (ii) the persistence of price changes from immediate to short timescales, revealing the interplay between returns, queue sizes, and orders’ queue positions. We document a fundamental trade-off: a negative correlation between maker fill likelihood and post-fill returns. This dictates that viable maker strategies often require a contrarian approach, counter-trading the prevailing order book imbalance. These dynamics render commonly-cited strategies highly unprofitable, leading us to model `Reversals’: situations where a contrarian maker strategy at the touch proves effective. ...

Why do financial prices exhibit Brownian motion despite predictable order flow? ArXiv ID: 2502.17906 “View on arXiv” Authors: Unknown Abstract In financial market microstructure, there are two enigmatic empirical laws: (i) the market-order flow has predictable persistence due to metaorder splitters by institutional investors, well formulated as the Lillo-Mike-Farmer model. However, this phenomenon seems paradoxical given the diffusive and unpredictable price dynamics; (ii) the price impact $I(Q)$ of a large metaorder $Q$ follows the square-root law, $I(Q)\propto \sqrt{“Q”}$. Here we theoretically reveal why price dynamics follows Brownian motion despite predictable order flow by unifying these enigmas. We generalize the Lillo-Mike-Farmer model to nonlinear price-impact dynamics, which is mapped to an exactly solvable Lévy-walk model. Our exact solution shows that the price dynamics remains diffusive under the square-root law, even under persistent order flow. This work illustrates the crucial role of the square-root law in mitigating large price movements by large metaorders, thereby leading to the Brownian price dynamics, consistently with the efficient market hypothesis over long timescales. ...

The “double” square-root law: Evidence for the mechanical origin of market impact using Tokyo Stock Exchange data ArXiv ID: 2502.16246 “View on arXiv” Authors: Unknown Abstract Understanding the impact of trades on prices is a crucial question for both academic research and industry practice. It is well established that impact follows a square-root impact as a function of traded volume. However, the microscopic origin of such a law remains elusive: empirical studies are particularly challenging due to the anonymity of orders in public data. Indeed, there is ongoing debate about whether price impact has a mechanical origin or whether it is primarily driven by information, as suggested by many economic theories. In this paper, we revisit this question using a very detailed dataset provided by the Japanese stock exchange, containing the trader IDs for all orders sent to the exchange between 2012 and 2018. Our central result is that such a law has in fact microscopic roots and applies already at the level of single child orders, provided one waits long enough for the market to “digest” them. The mesoscopic impact of metaorders arises from a “double” square-root effect: square-root in volume of individual impact, followed by an inverse square-root decay as a function of time. Since market orders are anonymous, we expect and indeed find that these results apply to any market orders, and the impact of synthetic metaorders, reconstructed by scrambling the identity of the issuers, is described by the very same square-root impact law. We conclude that price impact is essentially mechanical, at odds with theories that emphasize the information content of such trades to explain the square-root impact law. ...

Agent-Based Simulation of a Perpetual Futures Market ArXiv ID: 2501.09404 “View on arXiv” Authors: Unknown Abstract I introduce an agent-based model of a Perpetual Futures market with heterogeneous agents trading via a central limit order book. Perpetual Futures (henceforth Perps) are financial derivatives introduced by the economist Robert Shiller, designed to peg their price to that of the underlying Spot market. This paper extends the limit order book model of Chiarella et al. (2002) by taking their agent and orderbook parameters, designed for a simple stock exchange, and applying it to the more complex environment of a Perp market with long and short traders who exhibit both positional and basis-trading behaviors. I find that despite the simplicity of the agent behavior, the simulation is able to reproduce the most salient feature of a Perp market, the pegging of the Perp price to the underlying Spot price. In contrast to fundamental simulations of stock markets which aim to reproduce empirically observed stylized facts such as the leptokurtosis and heteroscedasticity of returns, volatility clustering and others, in derivatives markets many of these features are provided exogenously by the underlying Spot price signal. This is especially true of Perps since the derivative is designed to mimic the price of the Spot market. Therefore, this paper will focus exclusively on analyzing how market and agent parameters such as order lifetime, trading horizon and spread affect the premiums at which Perps trade with respect to the underlying Spot market. I show that this simulation provides a simple and robust environment for exploring the dynamics of Perpetual Futures markets and their microstructure in this regard. Lastly, I explore the ability of the model to reproduce the effects of biasing long traders to trade positionally and short traders to basis-trade, which was the original intention behind the market design, and is a tendency observed empirically in real Perp markets. ...

Market Making with Fads, Informed, and Uninformed Traders ArXiv ID: 2501.03658 “View on arXiv” Authors: Unknown Abstract We characterise the solutions to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads – these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad, we model how informed traders and uninformed traders arrive in the market. The market maker knows of the two groups of traders but only observes the anonymous order arrivals. We study both, the complete information and the partial information versions of the control problem faced by the market maker. In such frameworks, we characterise the value of information, and we find the price of liquidity as a function of the proportion of informed traders in the market. Lastly, for the partial information setup, we explore how to go beyond the Kalman-Bucy filter to extract information about the fad from the market arrivals. ...

High-frequency lead-lag relationships in the Chinese stock index futures market: tick-by-tick dynamics of calendar spreads ArXiv ID: 2501.03171 “View on arXiv” Authors: Unknown Abstract Lead-lag relationships, integral to market dynamics, offer valuable insights into the trading behavior of high-frequency traders (HFTs) and the flow of information at a granular level. This paper investigates the lead-lag relationships between stock index futures contracts of different maturities in the Chinese financial futures market (CFFEX). Using high-frequency (tick-by-tick) data, we analyze how price movements in near-month futures contracts influence those in longer-dated contracts, such as next-month, quarterly, and semi-annual contracts. Our findings reveal a consistent pattern of price discovery, with the near-month contract leading the others by one tick, driven primarily by liquidity. Additionally, we identify a negative feedback effect of the “lead-lag spread” on the leading asset, which can predict returns of leading asset. Backtesting results demonstrate the profitability of trading based on the lead-lag spread signal, even after accounting for transaction costs. Altogether, our analysis offers valuable insights to understand and capitalize on the evolving dynamics of futures markets. ...