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Author: Ihsan Badshah
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The purpose of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surfaces. The approach is similar to that of the Dumas, Fleming and Whaley (DFW) (1998) study. We use moneyness in implied forward price and out-of-the-money put-call options on the FTSE 100 stock index. After adjustments, a nonlinear parametric optimization technique is used to estimate different DFW models to characterize and produce smooth implied volatility surfaces. Next, principal component analysis is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surfaces. We then estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smirk(skew) and time to maturity. We find the constant volatility model fails to explain the variations in the surfaces. However, the first three principal components (or factors) can explain about 69-88% of the variances in the implied volatility surfaces: in which on average 56% explains by the level factor, 15% by the term structure factor, and additional 7% by the jump-fear factor. The applications of our study can be in options trading, hedging of derivatives positions, risk management of options, and policy making.
Author: Ihsan Badshah
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The purpose of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surfaces. The approach is similar to that of the Dumas, Fleming and Whaley (DFW) (1998) study. We use moneyness in implied forward price and out-of-the-money put-call options on the FTSE 100 stock index. After adjustments, a nonlinear parametric optimization technique is used to estimate different DFW models to characterize and produce smooth implied volatility surfaces. Next, principal component analysis is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surfaces. We then estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smirk(skew) and time to maturity. We find the constant volatility model fails to explain the variations in the surfaces. However, the first three principal components (or factors) can explain about 69-88% of the variances in the implied volatility surfaces: in which on average 56% explains by the level factor, 15% by the term structure factor, and additional 7% by the jump-fear factor. The applications of our study can be in options trading, hedging of derivatives positions, risk management of options, and policy making.
Author: Rama Cont
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
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.
Author: Matthias R. Fengler
Publisher: Springer Science & Business Media
ISBN: 3540305912
Category : Business & Economics
Languages : en
Pages : 232
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Book Description
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.
Author: Jim Gatheral
Publisher: John Wiley & Sons
ISBN: 1118046455
Category : Business & Economics
Languages : en
Pages : 204
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Book Description
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: Ricardo Baeza-Yates
Publisher: Springer Science & Business Media
ISBN: 0387233946
Category : Mathematics
Languages : en
Pages : 497
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Book Description
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.
Author: Les Clewlow
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the number of shocks that move the whole implied volatility surface, their interpretation and their correlation with percentage changes in the underlying asset. This work differs from Skiadopoulos, Hodges and Clewlow (1998) in which they looked at the dynamics of smiles for a given maturity bucket. We look at daily changes in implied volatilities under two different metrics: the strike metric and the moneyness metric. Since we are dealing with a three dimensional problem, we fix ranges of days to maturity, we pool them together and we apply the Principal Components Analysis (PCA) to the changes in implied volatilities over time across both the strike (moneyness) metric and the pooled ranges of days to maturity. We find similar results for both metrics. Two shocks explain the movements of the volatility surface, the first shock being interpreted as a shift, while the second one has a Z-shape. The sign of the correlation of the first shock with percentage changes in the underlying asset depends on the metric that we look at, while the sign is positive under both metrics regarding the second shock. The results suggest that the number of shocks, their interpretation and the sign of their correlation with changes in the underlying asset is the same for the whole implied volatility surface as it is for the smile corresponding to a fixed maturity bucket.
Author: Jim Gatheral
Publisher:
ISBN: 9781119202073
Category : Options (Finance)
Languages : en
Pages : 179
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Book Description
Author: Riccardo Rebonato
Publisher: John Wiley & Sons
ISBN: 0470091401
Category : Business & Economics
Languages : en
Pages : 864
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Book Description
In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School
Author: Matthias R. Fengler
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.
Author: Rama Cont
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
We propose a market-based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random factors. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data on SP500 and DAX options.We illustrate how this approach extends and improves the accuracy of the well-known 'sticky moneyness' rule used by option traders for updating implied volatilities. Our approach gives a justification for the use of 'Vegas' for measuring volatility risk and provides a decomposition of volatility risk as a sum of independent contributions from empirically identifiable factors.
