Analysis of aggregated tick returns: evidence for anomalous diffusion

Area of Science:

• Quantitative Finance
• Statistical Modeling
• Market Microstructure

Background:

• Stock price changes exhibit heavy-tailed distributions, indicating frequent extreme events.
• Trading frequency alone does not fully explain these large price fluctuations.

Purpose of the Study:

• Investigate the underlying causes of significant stock price volatility.
• Analyze stock price dynamics beyond trading frequency in NASDAQ stocks.

Main Methods:

• Analysis of stock price changes for ten NASDAQ stocks in 2002.
• Examination of trading intervals with a fixed number of trades to isolate factors.
• Modeling price movement as a discrete diffusion process in tick time.

Main Results:

• Stock prices follow a discrete diffusion process with variable step width in tick time.
• The mean step width, representing single-trade returns, is a key determinant of large aggregate returns.
• A statistical model incorporating step width asymmetries and correlations accurately reproduces empirical return distributions.

Conclusions:

• Trading frequency is insufficient to explain heavy-tailed stock price distributions.
• The variability and characteristics of single-trade returns (step width) are crucial for understanding aggregate price movements.
• A comprehensive statistical model accounting for asymmetries and correlations provides accurate predictions of stock return distributions.