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

Academic year 2025/2026
Lecturer Fabrizio Lillo, Giorgio Rizzini

Examination procedure

<p>Oral exam and seminar</p>

Syllabus

Market Microstructure


Electronic markets and limit order book. High frequency data. Statistical and structural models (Roll and its generalizations). Asymmetric information models (Glosten-Milgrom, Kyle). Information share. Inventory management models. Optimal market making strategies. Statistical limit order book models and scenario generation. Trading models: Market impact and order flow. Trading costs. Optimal execution strategies. High Frequency Trading. High Frequency Econometrics: Realized volatility and 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. Models of random graphs: Erdos Renyi graphs, Exponential random graphs, Stochastic block model, configuration model. Maximum entropy principle and networks. Networks from time series.


Systemic risk


Mechanisms for systemic risk and models: 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 cojumps


Bibliographical references

Notes and papers selected during the course


-- 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