Backward jump continuous-time random walk: an application to market trading.

Area of Science:

• Quantitative Finance
• Stochastic Modeling
• Market Microstructure

Background:

• Continuous-time random walk (CTRW) models are used to describe complex systems.
• Understanding high-frequency stock price dynamics, especially in moderately liquid markets, remains a challenge.
• The bid-ask bounce phenomenon influences price movements but is not fully integrated into existing models.

Purpose of the Study:

• To derive a modified continuous-time random walk model incorporating backward jumps and negative feedback for stock price evolution.
• To model the stochastic behavior of share prices on a stock exchange at a high-frequency time scale.
• To validate the model using empirical data and identify key drivers of market dynamics.

Main Methods:

• Development of a backward jump modification to the continuous-time random walk model.
• Application of the model to describe spatiotemporal share price evolution in moderately liquid stock markets.
• Validation through comparison of the theoretical velocity autocorrelation function with empirical data from continuous quotations.

Main Results:

• The derived model successfully describes stochastic share price evolution on a high-frequency time scale.
• Satisfactory agreement was found between the model's theoretical velocity autocorrelation function and empirical data.
• A sharp backward correlation, reminiscent of the bid-ask bounce phenomenon, was identified as a key factor.

Conclusions:

• The backward jump modification of the CTRW model effectively captures the dynamics of moderately liquid stock markets.
• The identified backward correlation, linked to the bid-ask bounce, appears to dominate market behavior in such conditions.
• The model's principles may extend to other fields exhibiting contrarian behavior, such as those governed by the Le Chatelier-Braun principle.