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

TL;DR

This study models intraday limit order price change dynamics across different market caps using Markov chains, revealing systematic patterns and temporal phases that inform adaptive trading strategies.

Contribution

It introduces a Markov chain framework to analyze intraday price change transitions across market caps, uncovering temporal phases and capitalization effects on order stability.

Findings

Price inertia peaks during opening and closing hours

HMC stocks exhibit stronger inertia than LMC stocks

Distinct temporal phases identified on bid and ask sides

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.