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

Paper: arXiv 2601.04959

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (232)

1. High-frequency stock market order transitions during the US–China trade war 2018: A discrete-time Markov chain analysis (2024)
2. Market microstructure: A survey of microfoundations, empirical results, and policy implications (2005)
3. Stochastic models of limit order markets (2010)
4. A dynamic model of the limit order book (2009)
5. Studies of the limit order book around large price changes (2009)
6. Do liquidity measures measure liquidity? (2009)
7. An empirical analysis of stock and bond market liquidity (2005)
8. Time series analysis (1994)

0 of 232 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.