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

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.

Volatility Surface and Term Structure
Volatility Surface and Term Structure

Author: Kin Keung Lai

Publisher: Routledge

Published: 2013-09-11

Total Pages: 113

ISBN-13: 1135006989

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This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

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.

Fitting Local Volatility: Analytic And Numerical Approaches In Black-scholes And Local Variance Gamma Models
Fitting Local Volatility: Analytic And Numerical Approaches In Black-scholes And Local Variance Gamma Models

Author: Andrey Itkin

Publisher: World Scientific

Published: 2020-01-22

Total Pages: 205

ISBN-13: 9811212783

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The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.

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.

Semiparametric Modeling of Implied Volatility
Semiparametric Modeling of Implied Volatility

Author: Matthias R. Fengler

Publisher: Springer Science & Business Media

Published: 2005-12-19

Total Pages: 232

ISBN-13: 3540305912

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This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.