Intraday order transition dynamics in high, medium, and low market cap stocks: A Markov chain approach

ArXiv ID: 2502.07625 “View on arXiv”

Authors: Unknown

Abstract

An empirical stochastic analysis of high-frequency, tick-by-tick order data of NASDAQ100 listed stocks is conducted using a first-order discrete-time Markov chain model to explore intraday order transition dynamics. This analysis focuses on three market cap categories: High, Medium, and Low. Time-homogeneous transition probability matrices are estimated and compared across time-zones and market cap categories, and we found that limit orders exhibit higher degree of inertia (DoI), i.e., the probability of placing consecutive limit order is higher, during the opening hour. However, in the subsequent hour, the DoI of limit order decreases, while that of market order increases. Limit order adjustments via additions and deletions of limit orders increases significantly after the opening hour. All the order transitions then stabilize during mid-hours. As the closing hour approaches, consecutive order executions surge, with decreased placement of buy and sell limit orders following sell and buy executions, respectively. In terms of the differences in order transitions between stocks of different market cap, DoI of orders is stronger in high and medium market cap stocks. On the other hand, lower market cap stocks show a higher probability of limit order modifications and greater likelihood of submitting sell/buy limit orders after buy/sell executions. Further, order transitions are clustered across all stocks, except during opening and closing hours. The findings of this study may be useful in understanding intraday order placement dynamics across stocks of varying market cap, thus aiding market participants in making informed order placements at different times of trading hour.

Keywords: Markov chain, order transition dynamics, inertia (DoI), limit orders, market orders, equities

Complexity vs Empirical Score

• Math Complexity: 5.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs a Markov chain model, which involves matrix algebra and probability theory, placing it in the medium-high math complexity range. Empirically, it uses high-frequency tick-by-tick order data from NASDAQ100 stocks, conducts statistical analysis with transition matrices and Jensen-Shannon divergence, and presents findings on order dynamics, indicating strong data/implementation-heavy rigor.

  flowchart TD
    Start(["Research Goal: Analyze Intraday Order Transition Dynamics"]) --> Data["Data Source: High-Frequency Tick-by-Tick Data\nNASDAQ100 Stocks"]
    Data --> Category{"Categorize Stocks by\nMarket Cap"}
    Category --> H["High Market Cap"]
    Category --> M["Medium Market Cap"]
    Category --> L["Low Market Cap"]
    
    H --> Method
    M --> Method
    L --> Method
    
    Method["Methodology: First-Order\nDiscrete-Time Markov Chain"] --> Compute["Compute Time-Homogeneous\nTransition Probability Matrices"]
    Compute --> Analysis["Analysis: Compare DoI & Transitions\nacross Time Zones & Cap Categories"]
    
    Analysis --> Findings{"Key Findings"}
    
    Findings --> F1["Inertia (DoI) peaks at opening\n(Limit Orders dominant)"]
    Findings --> F2["Subsequent hour: DoI shifts\n(Limit decreases, Market increases)"]
    Findings --> F3["Mid-hours: Transitions stabilize"]
    Findings --> F4["Closing hour: Execution surge\n(Limit placement drops)"]
    Findings --> F5["Cap Differences: High/Med have\nstronger DoI; Low have more\nmodifications/executions"]