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

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.

The Behaviour of Implied Volatility Surface
The Behaviour of Implied Volatility Surface

Author: Amine Bouden

Publisher:

Published: 2006

Total Pages: 22

ISBN-13:

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In this paper, I investigate Implied Volatility Surface patterns for Call options on crude oil futures. Instead of studying the power of the large number of explanatory factors inherent to oil markets, I focus on the common characteristics of option prices. By using quadratic Implied Volatility Functions (IVFs), I aim to establish a mapping from implied volatilities to option's intrinsic characteristics i.e. moneyness and time to expiration and to test the capacity of these functions to provide a good forecast of option prices. I found that the profile of crude oil implied volatility is too complex to be fully explained by IVFs. The main contribution of the paper is to perform an econometric explanatory analysis on a high volatile market, the petroleum market.

Dynamics of the Implied Volatility Surface
Dynamics of the Implied Volatility Surface

Author: Jacinto Marabel Romo

Publisher:

Published: 2014

Total Pages: 22

ISBN-13:

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I perform a regression analysis to test two of the most famous heuristic rules existing in the literature about the behavior of the implied volatility surface. These rules are the sticky delta rule and the sticky strike rule. I present a new specification to test the sticky strike rule, which allows for dynamics in the implied volatility surface. In the empirical application I use monthly implied volatility surfaces corresponding to the IBEX 35 index. The estimation results show that the extended specification for the sticky strike rule presented in this article represents better the behavior of the implied volatility under this rule. Furthermore, there is not one rule which is the most appropriate at all times to explain the evolution of implied volatility surface. Depending on the market situation a rule may be more appropriate than another one. In particular, when the underlying asset displays trend, the sticky delta rule tends to prevail against the sticky strike rule. Conversely, when the underlying asset moves in range, then the sticky strike rule tends to predominate.

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.

Volatility Surfaces
Volatility Surfaces

Author: Wulin Suo

Publisher:

Published: 2014

Total Pages:

ISBN-13:

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Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.

Dynamics of Implied Volatility Surfaces
Dynamics of Implied Volatility Surfaces

Author: Rama Cont

Publisher:

Published: 2002

Total Pages: 36

ISBN-13:

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The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modeling approaches, giving rise to quot;Vegaquot; risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate how this approach model and improves the the well-known quot;sticky moneynessquot; rule used by option traders for updating implied volatilities. Our approach gives a justification for use of quot;Vegasquot; for measuring volatility risk and provides a decomposition of volatility risk as a sum of contributions from empirically identifiable factors.

The Volatility Smile
The Volatility Smile

Author: Emanuel Derman

Publisher:

Published: 2016

Total Pages:

ISBN-13: 9781119289258

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"The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options 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"--