ST461      Half Unit
Mathematics of Market Microstructure

This information is for the 2025/26 session.

Course Convenor

Availability

Requisites

Pre-requisites:

Students must have completed ST409 before taking this course.

This course delves into the advanced mathematical frameworks and techniques used in modern market microstructure modelling.  Students will explore the fundamentals  of stochastic processes with and without jumps, which are essential for understanding order arrival and price formation processes in financial markets.  Furthermore, students will learn to formulate and solve optimization problems under uncertainty. This includes understanding the Hamilton-Jacobi-Bellman equation, a cornerstone of dynamic programming. Equipped with this understanding the students will then go on to investigate the following topics in the first part of the course:

1. Inventory models, market liquidity, price impact without asymmetric information, market making in absence of asymmetric information. 

2. Optimal execution a la Almgren-Chriss and Obizhaeva and Wang.

3. Avellaneda and Stoikov model of limit order book.

The second part of the course  is dedicated to market equilibrium under asymmetric information in continuous time. This requires knowledge of stochastic filtering to estimate unobservable factors in a financial system using Kalman filtering techniques.  In particular, the  students will study

1.The Kyle model in continuous time and its extensions.

2. The sequential trading model of  Glosten and Milgrom model,  and its continuous-time extension,

3. Glosten model of electronic trading in limit order books.

Given this background,  in the third part of the course, the students will have opportunity to explore the most recent challenges in market microstructure such as decentralised exchanges, automated market making, and dark pools.

Overall, this course combines rigorous theoretical foundations with practical applications, preparing students for the complex challenges of quantitative finance.

20 hours of seminars in the Winter Term.

This course has a reading week in Week 6 of Winter Term.

10 Weeks of 3-hour seminars blending theory and practice. 

One problem set during week 6 that students will be given feedback on.

U. Cetin and A. Danilova. Dynamic Markov Bridges and Market Microstructure: Theory and Applications.

A. Cartea and S. Jaimungal. Algorithmic and High-frequency trading.

K. Back. Asset Pricing and Portfolio Choice Theory

R. Liptser and A. Shiryaev. Statistics of Random Processes I.

B. Oksendal and A. Salem. Applied Stochastic Control of Jump Diffusions

K. Webster. Handbook of Price Impact Modeling.

Presentation (30%) in Winter Term Week 9

This component of assessment includes an element of group work.

Problem sets (40%) in Winter Term Week 11

Project (30%) in Spring Term Week 1

The material will be assessed via a combination of in-class  problem set, group presentation of a theoretical model chosen from the list of papers provided, and a computational project.