Rough Volatility: 2 (Financial Mathematics)

Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. This mathematical description has been an active topic of research for decades, however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility is path-dependent and exhibits jump-like short-term behavior.

The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling and providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject's development and progression.

Christian Bayer is a senior researcher at the Weierstrass Institute for Applied Analysis and Stochastics, a public research institute in applied mathematics based in Berlin. He is on the editorial board of Quantitative Finance and is a member of the Council of the Berlin mathematics research center MATH+. He is an expert in stochastic numerics, applied probability, and computational finance, and his current research interests include the mathematics of implied volatilities, stochastic optimal control and machine learning for non-Markovian processes, efficient simulation and Fourier based option pricing, and rough path analysis.

Peter K. Friz is Einstein Professor in Mathematics at Technische Universität Berlin and is affiliated with the Weierstrass Institute for Applied Analysis and Stochastics. He has worked as a quant at Merrill Lynch and held a readership in stochastic analysis and quantitative finance at Cambridge University before becoming a full professor in Germany. Peter has been a visiting professor at Cambridge University, ETH Zurich, and Ecole Polytechnique Paris. He has served on multiple journal editorial boards and has written two other books. His main areas of research include stochastic analysis, rough paths, and mathematical aspects of volatility modeling.Masaaki Fukasawa is professor of mathematics at the Graduate School of Engineering Science, Osaka University, having previously worked in the department of mathematics as associate professor. He also worked at ETH Zurich, Tokyo Metropolitan University, and Center for the Study of Finance and Insurance at Osaka University. He serves on four journal editorial boards. His current research interests include mathematical aspects of volatility modeling, option data analysis, decentralized finance, machine learning, and quantum computing.

Jim Gatheral is Presidential Professor of Mathematics at Baruch College, CUNY, teaching in the Master of Financial Engineering program. Prior to joining the faculty of Baruch College, he was a managing director at Bank of America Merrill Lynch and an adjunct professor at the Courant Institute, New York University. His current research focuses on volatility modeling and modeling equity market microstructure for algorithmic trading.Antoine Jacquier is a professor of mathematics at Imperial College London, working at the interface of stochastic analysis, statistics, numerical methods, and quantum computing with applications to quantitative finance. He is a course director of the MSc in Mathematics and Finance program at Imperial, a consultant for financial institutions and tech companies, and a member of the editorial board of several leading journals in mathematical finance. He has published many influential papers and books on both the theoretical aspects and the applications of quantitative finance.

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 focuses on statistical finance problems, regulatory issues, and risk management of derivatives. Mathieu is notably one of the most renowned experts on the quantitative analysis of market microstructure and high frequency trading. He has collaborations with various financial institutions, including investment banks, hedge funds, trading firms, regulators, and exchanges. He has published more than 80 articles on these subjects and is currently serving on the editorial boards of 11 journals.