Intraday Limit Order Price Change Transition Dynamics Across Market Capitalizations Through Markov Analysis

ArXiv ID: 2601.04959 “View on arXiv”

Authors: Salam Rabindrajit Luwang, Kundan Mukhia, Buddha Nath Sharma, Md. Nurujjaman, Anish Rai, Filippo Petroni

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.

Keywords: Limit Order Book, Markov Chain, High-Frequency Trading, Order Execution, Market Microstructure

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs a rigorous Markov chain framework with metrics like spectral gap and entropy rate, indicating moderate-to-high mathematical sophistication. It is heavily data-driven, using high-frequency NASDAQ100 tick data with clear empirical methodologies for estimation and validation, making it highly backtest-ready.
  flowchart TD
    Start["Research Goal: Analyze Intraday LOB Price Dynamics"] --> Data["Data: High-Frequency NASDAQ100 Tick Data"]
    Data --> Method["Method: Discrete-Time Markov Chain\n(Categorize price changes into 9 states)"]
    Method --> Process["Process: Estimate TPMs for 6 Intraday Intervals\n(High, Medium, Low Market Cap Stocks)"]
    Process --> Analysis["Analysis: Compute Markov Metrics\n(Spectral Gap, Entropy, Recurrence Times, JSD)"]
    Analysis --> Outcomes["Outcomes:<br/>1. Price Inertia Peaking at Open/Close<br/>2. HMC Strongest Inertia, LMC Widest Spreads<br/>3. Temporal Phases: Opening, Midday, Closing<br/>4. Bid-Ask Asymmetry & Stationary Distributions<br/>5. Closing Hour Most Distinct Phase"]