
Let’s learn from the data some fundamental facts about the order book
We review two classic models of the order book dynamics and fit them to the data
We’ll discuss the intuition behind the standard Bouchaud-Mézard-Potters model of the order book, along with a complete derivation of the formulas, and a calibration to the data
We simulate a basic, constant-spread market-making strategy, evaluate its performance, discover the limitations of this framework, and deduce fundamental rules for effective market making
In this lecture, you will get a full derivation of the foundational Avellaneda-Stoikov model of market-making from first principles
We compute from the data the market impact function and learn the link between spread and asymptotic market impact
We explore a comprehensive model of market impact that incorporates feedback from trades into the price process, and realistic behavior of the market-maker
We learn what classes of general market impact models are consistent with the absence of statistical arbitrage in the market
We simulate a liquidation problem and compare the costs associated with five different liquidation strategies under three scenarios: no drift in the stock price, positive drift, negative drift. We then draw conclusions and develop some intuition on this problem.
We provide a full theoretical answer, based on stochastic optimal control, on why the cheapest liquidation strategy we observed in our numerical experiment is indeed the optimal solution, in the case of no drift on the stock price
We compute the theoretically optimal solution of the liquidation problem in the general case, and explain how this ties out to the intuition we developed in Lesson 9
In this course, we put a definite emphasis on real-world cases and hands-on experience. Each section starts with an analysis of tick data and/or a numerical simulation, from which we develop an intuition for what the right approach should be. You get to download the Python scripts and data samples, and start experimenting with them right away.
Then, we introduce theoretical tools and models as needed -- always explained from first principles and fully worked-out computations -- in order to solve the particular problem studied in the section and get a deeper understanding of all its aspects.
Let’s dive right in!
Contents:
Order book: Statistics, Dynamics, and Modeling
1.1 Book size and shape — empirical observations
1.2 Diffusion models of the order book
1.3 The Bouchaud-Mézard-Potters model
Liquidity Provision: Market-Making and the Avellaneda-Stoikov Model
2.1 A basic market-making strategy; Fundamental rules of market-making
2.2 The Avellaneda-Stoikov model
Market Impact, Spread, Liquidity
3.1 Measuring market impact on trade data
3.2 A simple market impact model without feedback
3.3 A comprehensive model with feedback
Optimal Execution
4.1 The liquidation problem: numerical experiments
4.2 The case without drift: a stochastic control approach
4.3 The case with drift