Fokker-Planck description for the queue dynamics of large tick stocks

Area of Science:

• Quantitative Finance
• Statistical Mechanics
• Market Microstructure

Background:

• Understanding the complex dynamics of financial markets, particularly order book behavior, is crucial for accurate pricing and risk management.
• Existing models often struggle to capture the state-dependent nature and sudden 'jump' events observed in high-frequency trading data.

Purpose of the Study:

• To develop a statistically robust model for queue dynamics in large tick assets.
• To incorporate state dependence and jump events into a unified Fokker-Planck equation framework.
• To identify universal scaling properties in order book dynamics.

Main Methods:

• Development of a two-dimensional Fokker-Planck equation incorporating state-dependent drift and diffusion terms.
• Inclusion of 'jump' events as birth-death terms within the Fokker-Planck equation.
• Calibration of model parameters using high-frequency data on best quotes (bid and ask prices).

Main Results:

• The queue dynamics exhibit approximate scale invariance, with rescaled volume (current volume/average volume) being the key variable.
• The drift term in the rescaled volume dynamics shows a stable, universal two-dimensional structure (gradient and rotational components).
• This drift structure is identified as the primary driver of dynamical correlations between the ask and bid queues.

Conclusions:

• The proposed Fokker-Planck model provides a universal statistical description of large tick asset queue dynamics.
• Rescaled volume dynamics are invariant across different stocks and time periods, simplifying analysis.
• The identified drift structure offers new insights into the interplay between bid and ask queues in financial markets.