Quantitative Research • Stochastic Modelling • Numerical Methods
El Karoui Master 2025/2026 — Sorbonne Université & École Polytechnique. I am currently an intern at Groupe BPCE within the Equity Model Validation team, working on the calibration and implementation of LSV-HJM models using particle methods.
About
My current work focuses on stochastic volatility modelling, calibration and numerical implementation, with C++ development in a QuantLib-derived library.
I am also interested in market microstructure and more abstract mathematical questions. Selected work and research notes are presented below.
Research & interests
Interest in local stochastic volatility, stochastic rates, Monte Carlo methods, particle-based calibration and numerical stability in option pricing.
Design of event-level limit order book simulators with heterogeneous agents, stochastic liquidity regimes and inverse inference of latent market composition from observable order flow.
Work on probabilistic structures including anisotropic percolation, projection techniques and rigorous finite/infinite-volume arguments.
Work
A quantitative study focused on robust aggregation of cryptocurrency prices across fragmented venues, with an emphasis on market microstructure, noisy quotes and statistical reliability.
View case study →Numerical work around equity derivatives models combining local stochastic volatility, stochastic interest rates and calibration-oriented simulation.
View case study →Research-grade event-level simulator for modern electronic markets, combining a full limit order book, heterogeneous agents, stochastic liquidity and inverse modelling of hidden market composition.
View case study →Study of paths built from the maximum modulus principle, following points where a holomorphic function reaches its maximal modulus on admissible families of surrounding curves.
View note →Contact