It has been recently shown that volatility is rough, meaning that volatility sample paths are much rougher than those of a Brownian motion. This phenomenon has been reported over thousands of assets and leads to very efficient models for pricing and hedging derivatives.In this talk, we try to understand the mechanisms underlying this universal property of the volatility. We show that only a rough behavior of the volatility process can allow for viable financial markets.

Bio:

Mathieu Rosenbaum is full professor at Ecole Polytechnique since 2016, where he holds the chair "Analytics and Models for Regulation". He obtained his Ph.D from University Paris-Est in 2007. After being Assistant Professor at École Polytechnique, he became Professor at University Pierre et Marie Curie (Paris 6) in 2011. Mathieu's research mainly focuses on statistical finance issues such as volatility modeling, analysing market microstructure or designing statistical procedures for high frequency data. In particular, he is one of the organizers of the conference "Market Microstructure, Confronting Many Viewpoints", which takes place every two years in Paris. Mathieu has collaborations with various financial institutions, notably BNP-Paribas since 2004. He also has several editorial activities. He is one of the editors in chief of the journal "Market Microstructure and Liquidity" . Furthermore, he is managing editor for "Quantitative Finance" and associate editor for "Electronic Journal of Statistics", "Journal of Applied Probability", "Mathematical Finance"; "Mathematics and Financial Economics", "Statistical Inference for Stochastic Processes", "SIAM Journal in Financial Mathematics"," Springer Briefs" and "Statistics and Risk Modeling". He received the Europlace Award for Best Young Researcher in Finance in 2014 and the European Research Council Grant in 2015.