Main Lecture Courses

Contagion! The Spread of Systemic Risk in Financial Networks
Thomas Hurd 

This minicourse aims to provide a timely summary of a growing body of systemic risk research as well as a unified mathematical framework for the primary channels that can transmit damaging shocks through financial systems. Much of its contents are new, not having appeared previously in published journals. It intended to serve as a coherent guide of equal interest to quantitative finance practitioners, financial regulators and a broad range of academics including economists, physicists, applied mathematicians and computer scientists. The minicourse will cover a subset of the material contained in my new book, a draft of which can be found here. Minicourse Outline:
  • Cascade Mechanisms and Cascade Equilibrium. Definition and properties of the cascade models of Eisenberg-Noe 2001, the Gai-Kapadia 2010, and the Asset Fire Sale Model
  • Random Graph constructions: Erdos-Renyi graph, configuration graph, scale-free preferential attachment graphs and inhomogeneous random graphs.
  • Bootstrap percolation and the Watts 2002 model of information cascades.
  • Finance Cascade analytics: Random Financial Networks, the WOR condition, locally tree-like independence. Cascade Mapping Theorems.
  • Advanced analytics: other models of default and liquidity cascades.

Slides: Lectures


Large scale machine learning and tools from convex optimization
Stéphane Gaiffas 

This short course will explain some recent techniques for supervised learning, with a particular emphasis on optimization algorithms that are able to train models at a large scale, and in large dimensions. Some keywords are the following:
  • Supervised learning, classification, regression
  • Features selection in high dimension by convex programming
  • Tools for stochastic convex optimization and distributed optimization

Slides: Lectures 1-2 (Mon) Lectures 3-4 (Tue) a notebook iPython


Hawkes processes in finance
Emmanuel Bacry 

Hawkes processes are mutually exciting point processes that have proved successful in many domains. They have been used successfully for over 30 years for modeling seismic data. In the last decade many over applications were developed ranging from social network to neurobiology. In finance, they allow very natural modelization of high frequency data at both order book level and bid-ask level. The literature on the application of Hawkes processes to financial data is constantly growing. This course corresponds to an introduction to Hawkes processes, focusing on their applications to finance. The following are some topics that will be covered:
  • Definition and main properties of Hawkes processes
  • Simulation
  • Parametric and non parametric estimation
  • Some application in other fields than finance
  • A first microstructure model in 2 dimensions
  • Trading flow modeling in 2 dimensions
  • Model in higher dimensions
  • Response function and impact modeling


Local volatility/stochastic volatility - market models for the smile
Lorenzo Bergomi 

What type of model can be used practically for risk-managing derivatives? We consider models that include vanilla options as hedge instruments, along with the underlying himself.
  • We start with the local volatility model. Is it a usable model? What is the delta - is it the local volatility delta, the sticky-strike delta, or yet another delta? What is the delta of a vanilla option? Does it make sense to re-calibrate the local volatility model on a daily basis?
  • We then turn to local-stochastic volatility models. We will see that the majority of them are not usable models - unless a very specific condition is met.

Slides: Lectures


CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex, France, Tél: +33 1 69 33 46 00 Fax: +33 1 69 33 46 46