Rough Volatility

Christian Bayer · Peter K. Friz · Masaaki Fukasawa · Jim Gatheral · Antoine Jacquier · Mathieu Rosenbaum

2023年12月 · Financial Mathematics 第 2 冊 · SIAM

電子書

291

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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. The mathematical description of the volatility process 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 behaves essentially as a fractional Brownian motion with a small Hurst parameter.

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, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression.

This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.