Paris Bachelier Seminar


Aim: The Bachelier lectures are docotoral training also opened to researchers and practitioners who would like to follow a specialised high-level class in the field of mathematical finance.

Periodicity and location: The lectures take place at Institut Henri Poincaré between 9h and 11h, according to the schedule indicated in Schedule, before the Bachelier seminar.


Lecture of Benjamin Jourdain et Huyên Pham

(CERMICS-ENPC ; Université Paris-Diderot)

Friday 23/03, 30/03, 06/04 and 13/04

Equations de McKean Vlasov

Lecture of Charles-Albert Lehalle

(CFM & Imperial College London)

Friday 18/11, 25/11 and 2/12

Financial Intermediation at Any Scale for Quantitative Modelling

ABSTRACT: During this series of lectures, we will go from the role of the financial system described as a large network of intermediaries to a fine description of high frequency market makers. The role of regulation in the recent transformations of participants’ practices will be exposed too. The viewpoint taken is the one of a practitioner or a researcher who has to put in place models. Existing models will be reviewed, and new challenges and the stakes of possible improvements will be discussed. Important stylized facts and important mechanisms that models should reproduce will be exposed.


  • The Financial System as a Network of Intermediaries:
    • Risk transformation as the primary role of the financial system
    • Marking the market: the stakes of liquidity provision
    • First elements on the price formation process
  • Market Participants Main topics:
    • Who does what? and at which price?
    • Market impact of large orders
    • Quantitative models for common practices
  • Stylized Facts on Liquidity:
    • Seasonalities and stationarity
    • What orderbooks tell us on trading practices?
    • How to measure (and model) liquidity?
  • Optimal trading
    • Mean-Variance frameworks
    • The role of the control: trading speed or limit prices?
    • Main features of usual models


  • Market Microstructure in Practice. WSP 2014. Laruelle, Lehalle.
  • The Financial Mathematics of Market Liquidity, CRC 2016, Olivier Guéant
  • Algorithmic and High-Frequency Trading , CPU 2015, Cartea, Jaimungal, Penalva Papers
  • Market Microstructure knowledge needed to control an intra-day trading process, 2013, Lehalle (chapter).
  • Simulating and analyzing order book data: The queue-reactive model (Journal of the American Statistical Association, Vol. 10, No. 509. , 2 Dec 2015), doi:10.1080/01621459.2014.982278 by Huang, Lehalle, Rosenbaum
  • Market Impacts and the Life Cycle of Investors Orders, 2015, Bacry, Iuga, Lasnier, Lehalle (paper).

ABOUT THE AUTHOR: Charles-Albert Lehalle is Senior Research Advisor at Capital Fund Management (CFM, Paris) and a member of the CFM-Imperial Institute of Quantitative Finance. He was formerly Global Head of Quantitative Research at Crédit Agricole Cheuvreux, and Global Head of Quantitative Research on Market Microstructure in the Equity Brokerage and Derivative Department of Crédit Agricole Corporate Investment Bank.
With a Ph.D. And an HDR in applied mathematics Charles-Albert Lehalle lectures at the Pierre et Marie Curie "Probability and Finance" and the MASEF/ENSAE Masters in Paris.
Since the financial crisis, Charles-Albert has studied market microstructure evolution and regulatory changes in Europe and the US, and has provided research and expertise on these topics to investors, intermediaries and policy-makers such as the European Commission, the French Senate and the UK Foresight Committee. He has been a member of the Consultative Workgroup on Financial Innovation of the European Market Authority (ESMA) and is part of the Scientific Committee of the French regulator (AMF). Besides, he chairs Euronext’s Index Advisory Group, working on topics like Smart Beta and Factor Investing.
He has published many academic papers about the use of stochastic control and stochastic algorithms to optimize trading flows with respect to flexible constraints. He has also authored papers on post-trade analysis, market impact estimation and modelling the dynamics of limit order books. He co-authored the book "Market Microstructure in Practice".
and co-edited the book "Market Microstructure: Confronting Many Viewpoints", being co-organizer of the eponymous conference taking place every even year in December in Paris. Charles-Albert is one of the managing editors of the “Market Microstructure and Liquidity” academic journal.

Lecture of Mihail Zervos

(London School of Economics)

Friday 7/4, 21/4, 28/4 and 5/5

Continuous time contract theory models

ABSTRACT: We consider a number of models involving two parties, a principal and an agent. In practice, the principal can be the owner of a firm and the agent can be a manager that is hired to run the firm's operations. The two parties may share the same information or not. The first of these two cases gives rise to a risk sharing problem in which the principal optimally determines the precise actions that the agent has to follow. The second one gives rise to a problem that may involve moral hazard in the sense that the agent can take actions that are not in the best interest of the principal. We develop a complete analysis of the models we consider, with emphasis on the important ideas underlying their analysis. The four lectures are structured to be relatively independent.

Lecture of Johannes Muhle-Karbe

(University of Michigan)

Friday 12/5 and 19/5

Equilibrium models with frictions


    Part I: Equilibrium Liquidity Premia (Joint work with Bruno Bouchard, Masaaki Fukasawa, and Martin Herdegen) We study equilibrium returns in a continuous-time model, where heterogenous mean-variance investors trade subject to quadratic transaction costs. We show that the unique equilibrium is characterised by a system of coupled but linear forward backward stochastic differential equations. Explicit solutions obtain in a number of concrete settings. The corresponding liquidity premia compared to the frictionless case are mean reverting; they are positive if the more risk-averse agents are net sellers.

    Part II: A Risk-Neutral Equilibrium Leading to Uncertain-Volatility Pricing (joint work with Marcel Nutz)

    We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with strong aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.


Propagation of uncertainty

  • October 9: L. Tamellini, Introduction and Polynomial Chaos Expansion, Sparse grids. Slides.
  • October 16: F. Nobile, Sparse grids approximation, Sparse grids. Slides
  • November 6: G. Migliorati, Random L2 regression methods. Slides
  • November 13: Raul Tempone, Sparse grids in option pricing of basket options. Multilevel Monte Carlo-Multi index Monte Carlo. Slides part 1, slides part 2.
  • November 20: Alvaro Moraes, Pure jump processes and Multilevel Monte Carlo. Slides

Lecture of Pierre Del Moral


Friday 15/01, 22/01, 29/01 and 12/02

An introduction to Feynman-Kac integration and genealogical tree based particle models

Slides: Lecture 1, Lecture 2, Lecture 3, Lecture 4.
Labs (.sce): Lab 1, Lab 2.