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

Period of duration of course
Course info
Number of course hours
Number of hours of lecturers of reference
Number of hours of supplementary teaching

Type of exam

Oral exam and seminars


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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. Market making. Statistical limit order book models.
Trading models: Market impact and order flow. Trading costs. Optimal execution. 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.

Educational aims

The first goal of the course is to introduce the fundamental notions of market microstructure, network modeling, and financial systemic risk. The second goal is to present some recent contributions of the scientific literature and open problems. The third goal is to provide the student with the tool for the empirical and computational analysis of high frequency data and data relevant for systemic risk.  

Bibliographical references

Notes and papers selected during the course

J. Hasbrouck, Empirical Market Microstructure, Oxford University Press (2007)

A. Cartea, S. Jaimungal, J. Penalva, Algorithmic and High-Frequency 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