Program Overview

Mathematical Models for Quantitative Finance: Market Microstructure, Networks and Systemic Risk

Period of execution

The course will take place from January 2026 to May 2026.

Info about the course

• Course hours: 45
• Hours of responsible teachers: 45
• CFU: 7

Exam mode

The exam will consist of an oral test and a seminar report.

Lesson log

Access to the lesson register is available.

Teacher

The course will be taught by:

• Giorgio Rizzini
• Fabrizio Lillo

Program

The course will cover the following topics:

Market microstructure

• Electronic markets and limit order books
• High frequency data
• Statistical and structural models (Roll and his generalizations)
• Asymmetric information models (Glosten-Milgrom and Kyle)
• Information sharing
• Inventory models
• Optimal market making strategies
• Statistical models of the limit order book and scenario generation
• Trading Patterns: Market Impact and Order Flow
• Transaction costs
• Optimal execution
• High frequency trading
• High frequency econometrics: Volatility and realized covariance, microstructure noise, Point processes in finance (Hawkes processes and ACD models)

Financial networks

• Basic elements of graph theory
• Random walks on graphs
• Centrality measures
• Scale free networks and small world graphs
• Random graph models: ErdosRenyi graphs, Exponential random graphs, Stochastic block model, configuration model
• Maximum entropy principle and networks
• Time series networks

Systemic risk

• Mechanisms for systemic risk and their modeling: Bank runs, leverage cycles, interbank networks, Fire sales spillovers
• Econometric approaches to systemic risk: CoVar, MES, SRISK, Granger causality networks
• High frequency systemic risk: flash crashes, liquidity crises, systemic jumps

Training objectives

The course aims to:

1. Introduces the fundamental concepts of market microstructure, network models, and financial systemic risk.
2. Present recent contributions from the scientific literature and open problems.
3. Provide students with tools for empirical and computational analysis of high-frequency financial data and systemic risk data.

Bibliographical references

• J. Hasbrouck, Empirical Market Microstructure, Oxford University Press (2007)
• O. Gueant, The financial mathematics of market liquidity, Chapman & Hall (2016)
• A. Cartea, S. Jaimungal, J. Penalva, Algorithmic and HighFrequency Trading, Cambridge University Press (2015)
• M. Newman, Networks: an introduction, Oxford University Press (2010)
• J.-P. Fouque and J.A. Langsam, Handbook on Systemic Risk, Cambridge University Press 2013

Modules