We demonstrate in this talk that rough volatility is a consequence of no-statistical arbitrage constraints faced by market participants. To do so, we connect the shape of market impact curves to the behavior of the volatility. As a by-product, we are able to understand the celebrated square-root law of market impact and to understand the role of participation rate in this stylized fact of financial markets. This is joint work with Bruno Durin and Grégoire Szymanski.
Bio: Mathieu Rosenbaum is a full professor at École Polytechnique, where he holds the chair “Analytics and Models for Regulation” and is co-head of the quantitative finance (El Karoui) master program. His research mainly focuses on statistical finance problems, regulatory issues and risk management of derivatives. He published more than 80 articles on these subjects and supervised about 20 PhD students. He is notably a renowned expert on the quantitative analysis of market microstructure and high frequency trading. Mathieu Rosenbaum is also at the origin (with Jim Gatheral and Thibault Jaisson) of the development of rough volatility models. He is one of the editors in chief of the journal “Market Microstructure and Liquidity“and is associate editor for 10 other journals. Furthermore, he received the Europlace Award for Best Young Researcher in Finance in 2014, the European Research Council Grant in 2016, the Louis Bachelier prize in 2020 and the Quant of the Year award in 2021.