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Do Stock Orders Flock Together? An Empirical Analysis of Order
Arrival Rates using Hawkes’ Self-Exciting Point Process

Adviser: Jakub W. Jurek

Hyuk Soo Han

Economics

“When I finally found the answer to my thesis question, more thesis-worthy questions popped out. Now the problem was not to know where to start, but to decide where to stop. ...”


“Do you know why research is called research? You look for the answer, you don’t find the answer or another question pops up, and you re-do the search,” said my adviser one day in late March. Two weeks remaining till the deadline, I was still struggling to figure out how to clean up the optimization algorithm—not even the end product of my thesis, merely one of the tools I needed to answer my question. And that was not the biggest roadblock that hit me while I was working on the big T.

Returning as a spring-term senior after three years of absence and having skipped my sophomore year, I was coming back from a senior-year intersession longer than my entire stay in Princeton. While I needed to “refresh” myself with academics from years ago, I was bound to military duty in Korea until November. As I was not granted “student status” during my time away, I didn’t have access to any of the University resources until late January. I couldn’t even meet with my adviser until the beginning of the spring term, as my visa wouldn’t let me move in any earlier. I simply had to start from the other side of the planet—not just physically.

I wasn’t worried too much, however, as I thought I had a clear idea of what I wanted to research for my thesis. I planned to look at market liquidity as a key driver to the anomalies observed during the 2008 financial crisis and develop a model that explains my hypothesis. This soon became the biggest problem, as liquidity was too broad a concept with a number of different connotations. Moreover, I did not realize that it was a problem for months.

Because I wasn’t in Princeton, I had to rely solely on e-mail to communicate with my adviser, Professor Jakub Jurek. Professor Jurek suggested in his first e-mail that I focus on a more researchable topic, and he kept telling me that for the next three months. At first, I didn’t understand what he meant. Only in late December, I found out where I was standing—far from where I was supposed to be, having failed to figure out what exactly I wanted to write about.

I wrote Professor Jurek about my realization, and asked for help after not listening for months. After an hour-long phone call discussing my research interests and available resources, we came down to a list of sensible questions I might want to look at. I spent most of January on literature review, and decided to analyze the characteristics of intraday order arrival intensities on the New York Stock Exchange.

Even after choosing the right topic, the entire research process was far from easy. Time was a real problem, not only from the late start, but also from the nature of academic research. I had to work in the Data and Statistical Services (DSS) lab in the basement of Firestone Library, due to the specific format of my data. As I worked on some massive primary data whose size exceeded the available space of the stations in the lab, I had to download a set of the data, run some analysis, erase the dataset, and repeat with another. Since the lab was not open during the night, I spent most of my days and weekends down in the lab.

Once I finished retrieving relevant, analyzable data from the primary sources, I had to choose the ideal approach that not only gave good statistics but also was “codable-and-executable” on a personal computer, among a variety of theoretically plausible alternatives. Choosing the best optimization technique and writing the code took the longest among all other steps of the research. On the day I mentioned in the beginning, I went into Professor Jurek’s office around noon, we talked over the problem for hours, and the sun had set by the time I came out.

When I finally found the answer to my thesis question, more thesis-worthy questions popped out. Now the problem was not to know where to start, but to decide where to stop and move on to physical production of the thesis. Starting quantitative analysis two weeks before the due date, I had time to cover only some of the new questions.

I was lucky to have such an enthusiastic adviser, who was always there for me, ready and willing to help. Meeting me for the first time in February—we had never met before, as he came to Princeton during my time away—Professor Jurek helped me more than I ever expected from any professor. Introducing concepts I had never learned, bringing up questions, and thinking over unresolved problems together, he kept me motivated throughout the semester. I knocked on his door almost every week, first to ask for help, then to update my progress and discuss next steps, and by the end of the spring, just to talk.

The thesis was not only the biggest research project I have ever worked on, but also the proudest achievement I have ever had. It wasn’t just about developing a statistically significant stochastic model. Every step of the research was rewarding—coming up with questions, studying various tools for research, designing an algorithm that improves the efficiency of an optimization technique I had never heard of, and summing up all of the steps into one piece of work. My only regret is that I didn’t have time to address some of the issues that came to my mind too late.

At our last meeting, two days before the due date, Professor Jurek said, “The greatest part of the research is that, when you finally solve your question, you are the only one that knows the answer. Well, you’ll tell me when you do and I will know the answer, too.” I wouldn’t have understood him a few months earlier, but my response was, “Oh, yeah,” as I was done with my research. Well, almost done. I went back and added a couple of sections that I was not satisfied with. I was, so to speak, addicted to research by then—feeling lost when I finally submitted my final draft and thinking about the unresolved questions that remained for the next weeks.

My experience is not even close to the ideal example of senior thesis, or academic research in general. It should rather be labeled “do not try this at home,” in terms of topic selection, early communication with your adviser, and time management. Following the identical path will take many things away from you—sleep, relaxed meals, time to hang out with friends, and so on. You might have to wait outside Firestone in the morning in the rain to reserve a station in the un-air-conditioned DSS lab.

Some say history repeats, others say it doesn’t. I know for sure that there is one history that has repeated every year in Princeton history—some, yes, “some,” seniors repeat the same mistake I have made. But they all survived and learned from the mistake. There is one thing I could tell the next generation of ambitious Tigers about their theses—enjoy the challenge while it lasts.

Do Stock Orders Flock Together? An Empirical Analysis of Order
Arrival Rates using Hawkes’ Self-Exciting Point Process

Hyuk Soo Han

Jakub W. Jurek

Assistant Professor of Economics

“The thesis is a shared experience, and both parties should be learning something new during the process.”

Advising a senior thesis is a great way to share one’s passion for a subject, and, in particular, for the process of discovery. It is a unique opportunity to learn by apprenticeship, with the adviser acting as a guide, pointing out nuances, and helping make decisions. This results in an interaction that is much more open-ended and dynamic than what is typical of the classroom setting. The student not only has to be able to critically evaluate existing research, but to propose and test alternatives. 

I particularly enjoy putting a student in a position to become an expert on a topic of broad interest and practical relevance. Since students’ topics are generally distinct from my own research, advising provides me with a preview of some interesting new facts and data. This keeps me actively involved in the process, and effectively gives the student a chance to really experience being on the “sharp end”—to use climbing terminology—of the research process.

Research requires not only the intellectual maturity to select an interesting question, but also the perseverance and innate curiosity to execute the necessary analysis at a high level of precision. Hyuk Soo Han embodied these traits in just the right proportions to make advising him essentially effortless for me. Before soliciting advice, Hyuk always put tremendous effort into finding solutions to the problems he encountered—be it a mathematical derivation, or optimizing a piece of code to process the vast amounts of data he was working with.

Hyuk’s remarkable commitment was best evidenced to me by the fact that his final draft incorporated regressions and comments that I suggested only a day or two before the thesis was due. To put this into context, I should add that when I made those suggestions, I was blissfully unaware of the rapidly approaching deadline.

Hyuk was in a very unique situation; he was returning to the Princeton campus in January of his senior year, after having completed two years of military service in South Korea. Here was a student who would not only have to re-immerse himself in classwork after an extended hiatus and make new friends among his “adoptive” senior class, but also complete a thesis with one semester’s worth of direct supervision. 

Although these circumstances initially seemed to be an obstacle, they actually proved to be a useful disciplining device. Rather than spend the fall “playing” with data, Hyuk took the time to carefully refine his research topic and identify a series of testable hypotheses. This proved to be very valuable, as he could focus his attention in the spring on data and implementation issues.

Hyuk’s senior thesis examined clustering in the arrival of trade orders on the New York Stock Exchange, using a class of models originally designed to study earthquakes (“larger earthquakes beget larger aftershocks”). His project was notable along three dimensions. First, the modeling backbone of the thesis required the mastery of advanced methods from mathematics and statistics. Second, Hyuk improved on existing estimation methods for Hawkes models by recognizing a new recursive structure, which allowed him to considerably speed up computation. And, finally, he implemented his project using a vast data set of trade and quote data, finding strong evidence of clustering and subsequent return predictability. Hyuk’s ability to execute on both the theoretical and empirical sides of the project was remarkable. 

There are two key pieces of advice that I would pass along to future seniors. First, take your time to refine and formulate a concrete research hypothesis. Research is about posing and answering questions, not simply about critically evaluating an area; it is not a quantitative editorial. (I recall myself laboring over this while a senior—it took me the better part of five months to settle on my topic … and two weeks to write the thesis. I don’t necessarily recommend this ratio, but you get the point—a well-formulated topic will keep you excited and on point when it comes to executing the project.) Second, and perhaps more importantly, both you and your adviser should be passionate about the question. The thesis is a shared experience, and both parties should be learning something new during the process.