Download or read book Splines Implied Volatility Surfaces written by and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Empirical Performance of a Spline Based Implied Volatility Surface written by Gergely (Greg) Orosi and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a nonparametric spline based representation of the implied volatility surface and evaluate its empirical performance. Our findings indicate that the proposed model significantly outperforms the best performing implied volatility model reported in the current literature. We further contribute to the empirical finance literature by choosing a proper model evaluation criterion. By measuring the leave-one-out cross-validation model pricing error of the thin-plate spline-based model, we demonstrate that this superior performance is not the result of overfitting. Although we have previously shown that spline-based models have superior empirical performance, the models considered in this study have advantages over the previously considered models.
Download or read book Volatility Surfaces written by Wulin Suo and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of Implied Volatility Surfaces written by Marina Schnellen and published by . This book was released on 2007 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Models of Implied Volatility Surfaces written by Rama Cont and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Volatility Surface written by Jim Gatheral and published by John Wiley & Sons. This book was released on 2011-03-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Implied Volatility Functions written by Bernard Dumas and published by . This book was released on 1996 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.
Download or read book Advanced Equity Derivatives written by Sebastien Bossu and published by John Wiley & Sons. This book was released on 2014-05-19 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Download or read book Dynamic Factor Models for the Volatility Surface written by Michel van der Wel and published by . This book was released on 2016 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, (iii) for the restricted models option Delta is preferred over the more often used strike relative to spot price as measure for moneyness.
Download or read book Modeling the Dynamics of Implied Volatility Surfaces written by Ihsan Badshah and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book DSFM Fitting of Implied Volatility Surfaces written by Szymon Borak and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics of the Implied Volatility Surface written by Jacinto Marabel Romo and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stable Local Volatility Calibration Using Kernel Splines written by Cheng Wang and published by . This book was released on 2008 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes an optimization formulation to ensure accuracy and stability in the local volatility function calibration. The unknown local volatility function is represented by kernel splines. The proposed optimization formulation minimizes calibration error and an L1 norm of the vector of coefficients for the kernel splines. The L1 norm regularization forces some coefficients to be zero at the termination of optimization. The complexity of local volatility function model is determined by the number of nonzero coefficients. Thus by using a regularization parameter, the proposed formulation balances the calibration accuracy with the model complexity. In the context of the support vector regression for function based on finite observations, this corresponds to balance the generalization error with the number of support vectors. In this thesis we also propose a trust region method to determine the coefficient vector in the proposed optimization formulation. In this algorithm, the main computation of each iteration is reduced to solving a standard trust region subproblem.
Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Option Pricing Models and Volatility Using Excel VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2012-06-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland
Download or read book Option Implied Risk Neutral Distributions and Risk Aversion written by Jens Carsten Jackwerth and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
