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on Market Microstructure |
| By: | Salam Rabindrajit Luwang (National Institute of Technology Sikkim India); Kundan Mukhia (National Institute of Technology Sikkim India); Buddha Nath Sharma (National Institute of Technology Sikkim India); Md. Nurujjaman (National Institute of Technology Sikkim India); Anish Rai (Chennai Mathematical Institute Tamil Nadu India); Filippo Petroni (University G. d'Annunzio of Chieti-Pescara Italy) |
| Abstract: | Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency NASDAQ100 tick data. Employing a discrete-time Markov chain framework, we categorize consecutive price changes into nine states and estimate transition probability matrices (TPMs) for six intraday intervals across High ($\mathtt{HMC}$), Medium ($\mathtt{MMC}$), and Low ($\mathtt{LMC}$) market cap stocks. Element-wise TPM comparison reveals systematic patterns: price inertia peaks during opening and closing hours, stabilizing midday. A capitalization gradient is observed: $\mathtt{HMC}$ stocks exhibit the strongest inertia, while $\mathtt{LMC}$ stocks show lower stability and wider spreads. Markov metrics, including spectral gap, entropy rate, and mean recurrence times, quantify these dynamics. Clustering analysis identifies three distinct temporal phases on the bid side -- Opening, Midday, and Closing, and four phases on the ask side by distinguishing Opening, Midday, Pre-Close, and Close. This indicates that sellers initiate end-of-day positioning earlier than buyers. Stationary distributions show limit order dynamics are dominated by neutral and mild price changes. Jensen-Shannon divergence confirms the closing hour as the most distinct phase, with capitalization modulating temporal contrasts and bid-ask asymmetry. These findings support capitalization-aware and time-adaptive execution algorithms. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.04959 |
| By: | Sungwoo Kang |
| Abstract: | Building on the finding that Market Cap Normalization ($\SMC$) isolates the ``pure'' directional signal of informed trading \citep{kang2025}, this paper investigates the physics of how that signal is transmitted -- and how it breaks down. We employ \textbf{Tikhonov-regularized deconvolution} to recover the impulse response kernels of investor flows, revealing a dual-channel market structure: Foreign and Institutional investors act as ``architects'' of price discovery (positive permanent impact), while Individual investors act as liquidity providers (negative total impact). However, using \textbf{Multivariate Hawkes Processes}, we demonstrate that this structure is fragile. We find that individual investor order flow exhibits near-critical self-excitation (Branching Ratio $\approx$ 0.998). During periods of high retail herding, the market undergoes a \textbf{phase transition} into a ``critical state.'' In this regime, the signal-to-noise ratio collapses, causing the price impact of sophisticated investors to reverse from positive to negative. These findings suggest that retail contagion acts as a physical barrier that temporarily disables efficient price discovery. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.11602 |
| By: | Jo\~ao P. da Cruz |
| Abstract: | We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary relational system without assumed metric, temporal, or price coordinates. Observable quantities arise only through projection, implemented here via spectral embeddings of the graph Laplacian. A one-dimensional projection induces a price-like coordinate, while the projected density defines liquidity profiles around the mid price. Under a minimal single-scale hypothesis -- excluding intrinsic length scales beyond distance to the mid and finite visibility -- we show that projected supply and demand are constrained to gamma-like functional forms. In discrete data, this prediction translates into integrated-gamma cumulative profiles. We test these results using high-frequency Level~II data for several U.S. equities and find robust agreement across assets and intraday windows. Explicit comparison with alternative cumulative models using information criteria demonstrates a systematic preference for the integrated-gamma geometry. A minimal simulation of inflationary relational dynamics reproduces the same structure without invoking agent behavior or price formation mechanisms. These results indicate that key regularities of order-book liquidity reflect geometric constraints induced by observation rather than detailed microstructural dynamics. Supplementary Material is available at the arXiv submission. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.17245 |
| By: | Bastien Baude; Damien Challet; Ioane Muni Toke |
| Abstract: | We study the optimal liquidation of a large position on Uniswap v2 and Uniswap v3 in discrete time. The instantaneous price impact is derived from the AMM pricing rule. Transient impact is modeled to capture either exponential or approximately power-law decay, together with a permanent component. In the Uniswap v2 setting, we obtain optimal strategies in closed-form under general price dynamics. For Uniswap v3, we consider a two-layer liquidity framework, which naturally extends to multiple layers. We address the problem using dynamic programming under geometric Brownian motion dynamics and approximate the solution numerically using a discretization scheme. We obtain optimal strategies akin to classical ones in the LOB literature, with features specific to Uniswap. In particular, we show how the liquidity profile influences them. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.03799 |
| By: | Jo\~ao P. da Cruz |
| Abstract: | We introduce a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive market variables. The market is modeled as a relational substrate without assumed metric, temporal, or price coordinates. Observable quantities arise only through observation, implemented here as a reduction of relational degrees of freedom followed by a low-dimensional spectral projection. A one-dimensional projection induces a price-like coordinate and a projected liquidity density around the mid price, from which bid and ask sides emerge as two complementary restrictions. We show that directional liquidity imbalances decompose naturally into a rigid drift of the projected density and a geometric shear mode that deforms the bid--ask structure without inducing price motion. Under a minimal single-scale hypothesis, the shear geometry constrains the projected liquidity to a gamma-like functional form, appearing as an integrated-gamma profile in discrete data. Empirical analysis of high-frequency Level~II data across multiple U.S. equities confirms this geometry and shows that it outperforms standard alternative cumulative models under explicit model comparison and residual diagnostics. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.19369 |
| By: | Kim Christensen; Ulrich Hounyo; Mark Podolskij |
| Abstract: | In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump-diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general It\^o semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The $t$-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16613 |
| By: | Kim Christensen; Mark Podolskij; Nopporn Thamrongrat; Bezirgen Veliyev |
| Abstract: | In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16668 |