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 Implied Volatility Functions written by Joshua V. Rosenberg and published by . This book was released on 2008 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dumas, Fleming, Whaley (DFW, 1998) find that option models based on deterministic volatility functions (DVF) perform poorly because the estimated volatility function is unstable over time. DFW provide evidence that the DVF changes significantly on a weekly basis. This paper proposes a new class of dynamic implied volatility function models (DIVF). This classof models separates a time-invariant implied volatility function from the stochastic state variables that drive changes in the individual implied volatilities. The dynamics of the state variables are modeled explicitly. This framework facilitates consistent pricing and hedging with time-variation in the implied volatility function (IVF). In tests conducted using the full history of Samp;P500 futures option prices, the DIVF model is found to substantially improve pricing performance compared to static implied volatility function models and benchmark pricing models such as Black and Scholes (1973).
Download or read book Implied Volatility Functions written by Joshua Rosenberg and published by . This book was released on 1999 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implied Volatility Functions written by Veli-Matti Ahoranta and published by LAP Lambert Academic Publishing. This book was released on 2010-12 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evidences that there are volatility smiles and smirks in various financial markets suggest that Black and Scholes (1973) valuation formula is not completely valid. This thesis investigates implied volatility patterns and -functions on Finnish warrant market. The intention of the thesis is to find answers to the three following questions: what is the form of the volatility structure in Finnish warrant markets? Does there exist a better method to estimate volatilities than basic Black-Scholes constant volatility model? In case that there exist a superior method to estimate volatilities, is the method constantly best with every level of moneyness and time to expiration? To find answers to these questions a sample data is gathered from the year 2006 and then it is analysed by using statistical measurements. The analysis provides interesting findings about the existence of volatility structures in Finnish markets and it provides interesting insights to the Finnish warrant markets
Download or read book Implied Volatility Functions for One factor and Two factor Heath Jarrow and Morton Models written by I-Doun Terry Kuo and published by . This book was released on 2002 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Why do we smile on the determinants of the implied volatility function written by Ignacio Peña and published by . This book was released on 1997 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Financial Engineering written by Robert Kosowski and published by Academic Press. This book was released on 2014-11-26 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles of Financial Engineering, Third Edition, is a highly acclaimed text on the fast-paced and complex subject of financial engineering. This updated edition describes the "engineering" elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices. This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises. This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs. The Third Edition presents three new chapters on financial engineering in commodity markets, financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles and how to incorporate counterparty risk into derivatives pricing, among other topics Additions, clarifications, and illustrations throughout the volume show these instruments at work instead of explaining how they should act The solutions manual enhances the text by presenting additional cases and solutions to exercises
Download or read book Estimation of Smooth Volatility Functions in Option Pricing Models written by Yohan Kim and published by . This book was released on 2001 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Volatility Sneer written by D. Clive Thompson and published by . This book was released on 1997 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Heath Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models written by Kaushik I. Amin and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate various popular models of interest rate volatility and the Heath-Jarrow-Morton (HJM) approach to value interest rate derivatives by studying the information content and the forecast ability of HJM implied volatility in the Eurodollar futures options market. Implied volatility corresponding to the Ho-Lee, Courtadon, Cox-Ingersoll-Ross, Vasicek, and a linear proportional volatility model are examined within the HJM framework. The exercise compares these implied volatilities to a number of historical volatility benchmarks based on the GARCH model, the Glosten-Jagannathan-Runkle model, and several hybrid models combining the Cox-Ingersoll-Ross and Courtadon spot rate models and the GARCH and GJR approaches to model interest rate volatility. Our results show that there is a strong interaction effect between return shocks and the level of the interest rates in the volatility dynamics that none of the existing HJM volatility models and none of the GARCH type models can fully capture. Specifically, the impact of a shock to interest rate volatility is higher under a high interest rate than a low interest rate. The importance of implied volatility from the Ho-Lee, Courtadon, and Cox-Ingersoll-Ross models is significantly reduced after a term capturing the interaction effect is added to the volatility specification. The importance of implied volatility from the linear proportional and the Vasicek models is reduced but they can still explain a reasonably large portion of the time-variation in volatility.
Download or read book Why Do We Smile on the Determinants of the Implied Volatility Function written by Juan Ignacio Peña Sánchez de Rivera and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semiparametric Modeling of Implied Volatility written by Matthias R. Fengler and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Implied Adjusted Voladility Functions written by Hanani Farhah binti Harun and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implicit Volatilities written by Robert Schott and published by diplom.de. This book was released on 2008-10-23 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhaltsangabe:Introduction: Volatility is a crucial factor widely followed in the financial world. It is not only the single unknown determinant in the Black & Scholes model to derive a theoretical option price, but also the fact that portfolios can be diversified and hedged with volatility makes it a topic, which is crucial to understand for market participants comprising a wide group of private investors and professional traders as well as issuers of derivative products upon volatility. The year 1973 was in several respects a crucial year for implicit volatility. The breakdown of the Bretton-Wood-System paved the way for derivative instruments, because of the beginning era of floating currencies. Furthermore Fischer Black and Myron Samuel Scholes published in 1973 the ground breaking Black & Scholes (BS) model in the Journal of Political Economy. This model was adopted in 1975 at the Chicago Board Options Exchange (CBOE), which also was founded in the year 1973, for pricing options. Especially since 1973 volatility has become a tremendously debated topic in financial literature with continually new insights in short-time periods. Volatility is a central feature of option-pricing models and emerged per se as an independent asset class for investment purposes. The implicit volatility, the topic of the thesis, is a market indicator widely used by all option market practitioners. In the thesis the focus lies on the implicit (implied) volatility (IV). It is the estimation of the volatility that perfectly explains the option price, given all other variables, including the price of the underlying asset in context of the BS model. At the start the BS model, which is the theoretical basic of model-specific IV models, and its variations are discussed. In the concept of volatility IV is defined and the way it is computed is given as well as a look on historical volatility. Afterwards the implied volatility surface (IVS) is presented, which is a non-flat surface, a contradiction to the ideal BS assumptions. Furthermore, reasons of the change of the implied volatility function (IVF) and the term structure are discussed. The model specific IV model is then compared to other possible volatility forecast models. Then the model-free IV methodology is presented with a step-to-step example of the calculation of the widely followed CBOE Volatility Index VIX. Finally the VIX term structure and the relevance of the IV in practice are shown up. To ensure a good [...]
Download or read book Assessing the Performance of Symmetric and Asymmetric Implied Volatility Functions written by Panayiotis C. Andreou and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We seek to identify the best approach to model the daily implied volatility functions for pricing Samp;P 500 index options for the period 1996-2009. We compare the linear versus the nonlinear estimation approach, symmetric versus asymmetric model shapes with respect to the moneyness ratio, transformations of the underlying asset, and model estimation using joint datasets of calls and puts versus separating calls from puts. In-sample, we find models that are asymmetric functions of moneyness ratio work better, but out-of-sample the symmetric functions of the logarithmic transformation of the strike price are the best models. It is optimal to estimate the models nonlinearly and with the use of the joint dataset of out-of-money options instead of separating calls from puts. In contrast with other approaches that have been adopted in empirical research, the one we identify is consistent with the put-call-parity; hence, we avoid issues relating to model misspecification problems.
Download or read book Fitting Local Volatility Analytic And Numerical Approaches In Black scholes And Local Variance Gamma Models written by Andrey Itkin and published by World Scientific. This book was released on 2020-01-22 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Study of the Implied Volatility Function written by Qi Shi (M.Phil.) and published by . This book was released on 2005 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
