This project is the result of the collaboration between Mehdi and Joachim for one of our Ecole Polytechnique Research Projects (Fall 2021).
The goal of this project is to derive some preliminary results about rough volatility models, which are widely used to model financial markets. It is the result of a three-month research project by pair, during which we focused on the papers [1] and [2]. For each article, we successively mathematically analysed the model, and then implemented it in Python. All in all, this report should help anyone with basic background in stochastic calculus to understand the main ideas behind rough volatility models and verify them numerically through the provided Jupyter notebooks.
The final report is available under the pdf directory.
[1] Jim Gatheral Christian Bayer, Peter Friz, Pricing under rough volatility, 2015
[2] Omar El Euch, Eduardo Abi Jaber, Multi-factor approximation of rough volatility models, 2018