The Volatility Surface
The Volatility Surface

Author: Jim Gatheral

Publisher: John Wiley & Sons

Published: 2011-03-10

Total Pages: 204

ISBN-13: 1118046455

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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

Value Of Uncertainty, The: Dealing With Risk In The Equity Derivatives Market
Value Of Uncertainty, The: Dealing With Risk In The Equity Derivatives Market

Author: George J Kaye

Publisher: World Scientific Publishing Company

Published: 2012-11-16

Total Pages: 438

ISBN-13: 1908979585

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Along with the extraordinary growth in the derivatives market over the last decade, the impact of model choice, and model parameter usage, has become a major source of valuation uncertainty. This book concentrates on equity derivatives and charts, step by step, how key assumptions on the dynamics of stocks impact on the value of exotics. The presentation is technical, but maintains a strong focus on intuition and practical application./a

Recent Advances in Applied Probability
Recent Advances in Applied Probability

Author: Ricardo Baeza-Yates

Publisher: Springer Science & Business Media

Published: 2006-02-28

Total Pages: 497

ISBN-13: 0387233946

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Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.

The Volatility Smile
The Volatility Smile

Author: Emanuel Derman

Publisher: John Wiley & Sons

Published: 2016-09-06

Total Pages: 528

ISBN-13: 1118959167

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The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.

Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-implied and Realized Volatilities
Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-implied and Realized Volatilities

Author: Tim Bollerslev

Publisher:

Published: 2004

Total Pages: 60

ISBN-13:

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"This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment suggests that the procedure works well in practice. Implementing the procedure with actual S&P 500 option-implied volatilities and high-frequency five-minute-based realized volatilities results in significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of underlying macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns"--Abstract.

Trading and Pricing Financial Derivatives
Trading and Pricing Financial Derivatives

Author: Patrick Boyle

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-12-17

Total Pages: 298

ISBN-13: 1547401214

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Trading and Pricing Financial Derivatives is an introduction to the world of futures, options, and swaps. Investors who are interested in deepening their knowledge of derivatives of all kinds will find this book to be an invaluable resource. The book is also useful in a very applied course on derivative trading. The authors delve into the history of options pricing; simple strategies of options trading; binomial tree valuation; Black-Scholes option valuation; option sensitivities; risk management and interest rate swaps in this immensely informative yet easy to comprehend work. Using their vast working experience in the financial markets at international investment banks and hedge funds since the late 1990s and teaching derivatives and investment courses at the Master's level, Patrick Boyle and Jesse McDougall put forth their knowledge and expertise in clearly explained concepts. This book does not presuppose advanced mathematical knowledge, though it is presented for completeness for those that may benefit from it, and is designed for a general audience, suitable for beginners through to those with intermediate knowledge of the subject.

Implied Volatilities as Forecasts of Future Volatility, Time-Varying Risk Premia, and Returns Variability
Implied Volatilities as Forecasts of Future Volatility, Time-Varying Risk Premia, and Returns Variability

Author: Mikhail Chernov

Publisher:

Published: 2002

Total Pages: 32

ISBN-13:

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The unbiasedness tests of implied volatility as a forecast of future realized volatility have found implied volatility to be a biased predictor. We explain this puzzle by recognizing that option prices contain a market risk premium not only on the asset itself, but also on its volatility. Hull and White (1987) show using a stochastic volatility model that a call option price can be represented as an expected value of the Black-Scholes formula evaluated at the average integrated volatility. If we allow volatility risk to be priced, this expectation should be taken under the risk-neutral probability measure, and can be decomposed into the expectation with respect to the physical measure and the risk-premium term. This term is just a linear function of the unobservable spot volatility. The decomposition explains the bias documented in the empirical literature and shows that the realized and historical volatility, which are used in the tests, are in fact the estimates of the unobserved quadratic variation and spot volatility of the stock-return generating process. Therefore, the use of these estimates generates the error-in-the-variables problem. We generalize the above results from a stochastic volatility model to a model with multiple volatility and jump factors. We provide an empirical illustration based on two US equity indices and three foreign currency rates. We find, that when we take into an account the risk-premium and use efficient methods to estimate volatility, the unbiasedness hypothesis can not be rejected, and the point estimate of the loading on the implied volatility in the traditional regression is equal to 1.