Introduction

From 2015 to 2018, I was a PhD student in Probability and Mathematical Finance at CERMICS, Ecole des Ponts ParisTech, working on the Local and Stochastic Volatility (LSV) models with my advisor Benjamin Jourdain.

Research Topic

This PhD focuses on the calibration of local and stochastic volatility models.

According to Gyongy's theorem, a local and stochastic volatility (LSV) model calibrated to the European call prices for all positive strikes and maturities leads to a stochastic differential equation (SDE) which is non-linear in the sense of McKean.

In the industry, probabilistic particle methods provide a practical and efficient calibration procedure of LSV models, provided that the range of the stochastic volatility process is not too large.

But so far, no existence or uniqueness result is available for the SDE describing the calibrated LSV model. The objective of this PhD is therefore to analyze this kind of equation and its simulation.

Publications & Preprints

• B. Jourdain, A. Zhou. Existence of a calibrated regime switching local volatility model and new fake Brownian motions. Accepted in Mathematical Finance
• A. Agarwal, S. De Marco, E. Gobet, J. G. Lopes-Salas, F. Noubiagain, A. Zhou. Numerical approximations of McKean anticipative BSDEs arising in Initial Margin requirements. Accepted in ESAIM: Proceedings and Surveys
• B. Jourdain, A. Zhou. Discretization in time of a class of mean-field diffusions including the calibrated local and stochastic volatility model. In preparation
• F. Bourgey, S. De Marco, E. Gobet, A. Zhou.Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations. Submitted

Conferences and Talks

• 13th International Conference in Monte Carlo and Quasi Monte Carlo methods in scientific computing, Rennes, France, July 2018
• Colloque des Jeunes Probabilistes et Statisticiens, Ile d'Oléron, France, May 2018
• Les Probabilités de demain, Paris, France, May 2018
• Groupe de Travail MsMath, CERMICS, November 2017
• 10th European Summer School in Financial Mathematics, Dresden, Germany, August 2017
• CEMRACS Summer School and Research Project, Luminy, France, Summer 2017
• Séminaire de Probabilités et Statistiques, Université Paris 13, France, January 2017
• Séminaire des doctorants, CERMICS, September 2016
• 9th European Summer School in Financial Mathematics, Saint-Petersburg, Russia, August 2016
• 3rd Young Researchers Meeting in Probability, Numerics and Finance, Le Mans, France, June 2016

Teaching

• Probabilités, 1A Ecole des Ponts ParisTech (Lectures)
• Finance : Aspects mathématiques et numériques, 2A Ecole des Ponts ParisTech (Tutorials)
• Statistiques numériques et analyse de données, 2A Ecole des Ponts ParisTech (Lectures)

Seminars

In 2016 and 2017, I co organized with Marion Sciauveau and Laura Silva-Lopes the Young Researchers Seminar at CERMICS.

Curriculum

I am a former student of École Polytechnique and Pierre and Marie Curie University. A detailed resume can be found here (English version) or here (French version).

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