Christian Bayer - Böcker

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.

This Open Access volume offers an accessible entry point into the fast-growing field of signature methods in finance. It is written for early-career researchers and quantitatively minded practitioners—quant analysts and applied researchers—seeking a clear, practical introduction. It highlights recent developments and includes coding examples to help readers apply signature methods in practice.The advantages of modeling financial markets from a path-wise perspective, rather than as a traditional series of returns, are increasingly gaining recognition. Signature methods provide a parsimonious description of paths of stochastic processes and, through the signature kernel, open a rich and compelling framework at the interface between machine learning and mathematical finance.“I have been extraordinarily fortunate to work alongside brilliant collaborators throughout this journey, and this book beautifully reflects the richness of that shared contribution—for which I am deeply grateful.”—Prof Terry Lyons, University of Oxford, Imperial College, and PI of DataSig “This fascinating collection, dedicated to Terry Lyons, offers invaluable insights into signature methods and their many uses.” Jim Gatheral, Presidential Professor, Baruch College, Quant of the Year 2021"A timely and important contribution to the fast-growing field of signature methods, showcasing the theory and applications of these powerful ideas.” — Prof Ben Hambly, University of Oxford“An impressive book on signatures with articles by the most distinguished researchers in the field. A reference from day one." – Dr Hans Buehler, co-CEO XTX Markets, Quant of the Year 2022"This book provides a masterful exposition and development of signature methods in finance. It is concise, precise, and actionable. It will be an excellent source for anyone interested in modern financial engineering techniques." – Prof Alexander Lipton, Global Head of R&D, ADIA, and Founding Member ADIA Lab, Quant of the Year 2000 and Buy-side Quant of the Year 2021.