Modeling the Complex Dynamics of Financial Markets using a Physical System with Stochastic Properties
Physical and Biological Sciences
UCSC Physics Senior Thesis
The price dynamics of financial markets have long remained elusive. For over 100 years,
financial theory has relied on models of random price movement, reinforced by the efficient market hypothesis for asset pricing. Yet, decades of research show that financial markets exhibit anomalies that challenge a purely random model. These anomalies, including the "stylized facts" of fat-tail distributions and volatility clustering, are emblematic of excessive frequency of large returns and correlation in trade behavior. Using millisecond-stamped market depth data from the Chicago Mercantile Exchange (CME), price dynamics were analyzed for the S&P E-mini near-month futures contract. Market behavior during periods following scheduled announcements was compared to quiescent market periods, using both time-based and trade number-based returns. Fat-tail distributions were confirmed for time-based returns during active and quiet markets, with active markets showing higher leptokurtosis. Remarkably, trade number returns were highly Gaussian during quiet markets but developed fat-tails during economic news. This suggests that for a highly liquid broad market instrument such as the E-mini market activity is serially uncorrelated and essentially random during quiet periods, and that the anomalous stylized-facts emerge from announced news, in which new information informs the market and generates price changes. In addition, price returns were compared to a numerical simulation of a balancing process with an inverted pendulum, which is positioned between several forces and stabilized through stochastic noise. This physical model is known to exhibit behavior with properties that are qualitatively similar to financial markets, including the stylized facts. Using a stochastic differential equation with time-delayed feedback, the physical model was simulated and compared to the returns for the news-driven and quiet markets. A genetic algorithm was used to derive specific parameters that provide a very close fit to empirical data. We find that return distributions for both markets can be reproduced using this model based on a physical balancing process.
