Stochastic Volatility Models And Pricing Of Financial Deriatives
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| Author | : Jean-Pierre Fouque |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2011-09-29 |
| Genre | : Mathematics |
| ISBN | : 113950245X |
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
| Author | : Antoine Petrus Cornelius van der Ploeg |
| Publisher | : Rozenberg Publishers |
| Total Pages | : 358 |
| Release | : 2006 |
| Genre | : |
| ISBN | : 9051705778 |
| Author | : Jean-Pierre Fouque |
| Publisher | : Cambridge University Press |
| Total Pages | : 222 |
| Release | : 2000-07-03 |
| Genre | : Business & Economics |
| ISBN | : 9780521791632 |
This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
| Author | : Christian Kahl |
| Publisher | : Universal-Publishers |
| Total Pages | : 219 |
| Release | : 2008 |
| Genre | : Business & Economics |
| ISBN | : 1581123833 |
The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
| Author | : Frederic Abergel |
| Publisher | : Wiley |
| Total Pages | : 384 |
| Release | : 2015-05-04 |
| Genre | : Business & Economics |
| ISBN | : 9781119952244 |
Model calibration strategies and techniques for derivative products The calibration of derivatives has evolved significantly, covering new ground like implied volatility surface static and dynamics, first and higher-generation exotics calibration, local and stochastic volatility models, interest rates or multi-asset correlation modeling, default time modeling, credit derivatives, and more. This book introduces the fundamentals of model calibration by taking an intuitive approach to the Black, Scholes, and Merton and revisiting it in an incomplete markets setting, applying to a range of hedging strategies.
| Author | : Jim Gatheral |
| Publisher | : John Wiley & Sons |
| Total Pages | : 204 |
| Release | : 2011-03-10 |
| Genre | : Business & Economics |
| ISBN | : 1118046455 |
Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP
| Author | : Yue Kuen Kwok |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2022-05-08 |
| Genre | : Mathematics |
| ISBN | : 1000584275 |
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
| Author | : Christian Ekstrand |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2011-08-26 |
| Genre | : Business & Economics |
| ISBN | : 3642221556 |
This book gives a comprehensive introduction to the modeling of financial derivatives, covering all major asset classes (equities, commodities, interest rates and foreign exchange) and stretching from Black and Scholes' lognormal modeling to current-day research on skew and smile models. The intended reader has a solid mathematical background and is a graduate/final-year undergraduate student specializing in Mathematical Finance, or works at a financial institution such as an investment bank or a hedge fund.
| Author | : Lorenzo Bergomi |
| Publisher | : CRC Press |
| Total Pages | : 520 |
| Release | : 2015-12-16 |
| Genre | : Business & Economics |
| ISBN | : 1482244071 |
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
| Author | : Jerome Yen |
| Publisher | : Routledge |
| Total Pages | : 161 |
| Release | : 2014-11-27 |
| Genre | : Business & Economics |
| ISBN | : 1317638883 |
Exotic options and structured products are two of the most popular financial products over the past ten years and will soon become very important to the emerging markets, especially China. This book first discusses the products' recent development in the world and provides comprehensive overview of the major products. The book also discusses the risks of issuing and buying such products as well as the techniques to price them and to assess the risks. Volatility is the most important factor in determining the return and risk. Therefore, significant part of the book's content discusses how we can measure the volatility by using local and stochastic volatility models — Heston Model and Dupire Model, the volatility surface, the term structure of volatility, variance swaps, and breakeven volatility. The book introduces a set of dimensions which can be used to describe structured products to help readers to classify them. It also describes the more commonly traded exotic options with details. The book discusses key features of each exotic option which can be used to develop structured products and covers their pricing models and when to issue such products that contain such exotic options. This book contains several case studies about how to use the models or techniques to price and hedge risks. These case analyses are illuminating.
