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Rough volatility / edited by Christian Bayer, Peter K. Friz, Masaaki Fukasawa, Jim Gatheral, Antoine Jacquier, Mathieu Rosenbaum.
- Format:
- Book
- Series:
- Financial mathematics.
- Financial mathematics
- Language:
- English
- Subjects (All):
- Finance--Mathematical models.
- Finance.
- Uncertainty--Mathematical models.
- Uncertainty.
- Brownian motion processes--Mathematical models.
- Brownian motion processes.
- Brownian movements--Mathematical models.
- Brownian movements.
- Stochastic analysis.
- Physical Description:
- 1 online resource (xxviii, 263 pages).
- Place of Publication:
- Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) ; Alexandria, Virginia : American Statistical Association, [2024]
- System Details:
- Mode of access: World Wide Web.
- System requirements: Adobe Acrobat Reader.
- Summary:
- 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 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 and providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject's development and progression.
- Contents:
- Foreword / Jean-Philippe Bouchaud
- Foreword : roughness verses arbitrage / Walter Schachermayer
- Volatility is rough
- Pricing under rough volatility
- No-arbitrage implies power-law market impact and rough volatility
- Rough Heston
- Rough affine models
- Hedging under rough volatility
- Hybrid scheme for Brownian semistationary processes
- Asymptotics
- The forest expansion of forward variance models
- Regularity structure for rough volatility.
- Notes:
- Description based on title page of print version.
- Includes bibliographical references (pages 245-260) and index.
- ISBN:
- 1-61197-778-9
- Publisher Number:
- FM02 SIAM
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