Online

Foley, Michael

Mathematics

2014

MS

Since Benoit Mandelbrot's discovery of the fractal nature of financial price series, the quantitative analysis of financial markets has been an area of increasing interest for scientists, traders, and regulators. Further, major technological advances over this time have facilitated not only financial innovations, but also the computational ability to analyze and model markets. The stylized facts are qualitative statistical signatures of financial market data that hold true across different stocks and over many different timescales. In pursuit of a mechanistic understanding of markets, we look to accurately quantify such statistics. With this quantification, we can test computational market models against the stylized facts and run controlled experiments. This requires both discovery of new stylized facts, and a persistent testing of old stylized facts on new data. Using NASDAQ provided data covering the years 2008-2009, we analyze the trades of 120 stocks. An analysis of the stylized facts guides our exploration of the data, where our results corroborate other findings in the existing body of literature. In addition, we search for statistical indicators of market instability in our data sets. We find promising areas for further study, and obtain three key results. Throughout our sample data, high frequency trading plays a larger role in rapid price changes of all sizes than would be randomly expected, but plays a smaller role than usual during rapid price changes of large magnitude. Our analysis also yields further evidence of the long term persistence in the autocorrelations of signed order flow, as well as evidence of long range dependence in price returns.