Math 5440 Course Syllabus
This is a course on quantitative trading organized around the unifying topic of price impact. Price impact is a central phenomenon in trading that affects quantitative strategies over all horizons. Practitioners use price impact models in many finance applications.
Quantitative traders optimize and analyze the performance of their trading algorithms using live trading experiments and price impact models.
Quantitative portfolio managers leverage price impact models when building signals for statistical arbitrage and backtesting the performance of their strategies.
Risk managers and senior management measure the effect of price impact on portfolios to size their portfolios and mitigate liquidity risk during crises.
At the end of the course, students are expected to understand how to design live trading experiments, fit price impact models, and apply price impact models to a broad set of quantitative strategies. Emphasis is placed on communicating precise assumptions and actionable results to a general audience within the finance community.
The class is divided into three modules. The first module provides a brief primer to various related topics: trading terminology, the programming language q for the commonly used trading database kdb+, and the fundamental trading problems to solve. The second module studies real-life applications of price impact models within trading teams. It introduces and leverages a mathematical foundation of price impact rooted in stochastic analysis and stochastic control problems. Finally, the third module targets the empirical analysis of price impact and trading data. It identifies and solves common biases when fitting trading models and leverages the mathematical theory of causal inference to provide a rigorous statistical framework for live trading experiments.
The prerequisites of this class include Ito calculus, basic statistics, and a foundation in data analysis in python or R. Knowledge of causal inference, machine learning, stochastic control, kdb+, or market microstructure is not required at the start of the class.
Weekly breakdown
Module 1: Introduction (3 weeks)
What is price impact? Overview of finance applications and glossary of trading terms.
Preview of the two modules’ mathematics and data. Homework: read “direct estimation of equity market impact” by Almgren (2005), non-graded.
Primer on the database kdb+ and the programming language q. Homework: first coding steps in kdb+/q, non-graded.
Module 2: Using Price Impact Models (6 weeks)
Mathematical foundation of price impact. Example on the Obizhaevaand Wang (OW) model. Homework: proof-based exercises.
The generalized OW model. Absence of price manipulation. Homework: empirical estimation of a price impact model (code, 1/2).
Empirical review of price impact models. Homework: empirical estimation of a price impact model (code, 2/2).
Optimal execution. Homework: proof-based exercises.
Back testing and statistical arbitrage. Homework: backtesting rule-based strategies (code).
Risk management. Homework: backtesting a model-based strategy (code).
Module 3: Estimating Price Impact Models (5 weeks)
Bouchaud’s list of four causal trading biases. Introduction to live trading experiments. Homework: simulate a live trading experiment (code).
The Mathematics of causal inference (1/2). Homework: proof-based exercises.
The Mathematics of causal inference (2/2). Application to prediction bias. Homework: implement causal regularization for prediction bias (code).
Transaction Cost Analysis (TCA). Homework: read “The Non-Linear Market Impact of Large Trades” by Bershova and Rakhlin (2013) and “Causal Factor Investing: Can Factor Investing Become Scientific?” by Lopez de Prado (2022), proof-based exercises.
Further applications of causal inference and causal regularization. Cross impact. Homework: proof-based exercises.
Course Materials and Homework
The suggested reference material consists of slides provided by the lecturer, a review of articles in the literature, and the books Trades, Quotes, and Prices by Bouchaud et al. (2018, linkLinks to an external site.), and Q for mortals (linkLinks to an external site.). There are no required outside readings besides the three papers in the syllabus. Weekly homework, in the form of proof-based and code-based exercises, account for 100% of the grade. Each of the eleven homework assignments is worth 10 points, with the lowest grade dropped.
Class and University Policies
Academic integrity
Students must exhibit the highest level of personal and academic honesty and integrity in the course. You must always submit your own work and not that of others, except where group work is explicitly allowed or encouraged. When in doubt, consult the professor. Infractions will have serious consequences pursuant to the university’s rules.
Disabilities accommodations
If you have been certified by Disability Services to receive accommodations, please ask your liaison in GSAS to consult with your professor.
Email policy and Q&A forum
We will use Ed Discussion on CourseWorks to facilitate online discussion. The system is catered to getting you help fast and efficiently from classmates, the TAs, and myself. Rather than emailing questions directly to your TAs and me, we strongly encourage you to post your questions on Ed Discussion.