Psychological Arbitrage: An Analysis of the Dynamics of Apple's Stock Price in Neighborhoods of Round Numbers

Abstract

This research analyzes the dynamics of Apple's stock price movements around significant round numbers, predicts which round numbers are significant, and simulates stock price movements within these psychological market inefficiencies. It investigates the frequency distribution of Apple's stock price in the last three months of 2013, and examines the areas where stock prices tend to cluster or not cluster. Several mathematical models that replicate this phenomenon are designed and analyzed. Stochastic mean-reverting models are employed to simulate round number clustering effects as well as less conventional models that perturb volatility to produce desired movements in the stock price process. Trading strategies to exploit this effect are considered and tested against historical stock exchange data.