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 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 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 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 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 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 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 The Behaviour of Implied Volatility Surface written by Amine Bouden and published by . This book was released on 2006 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Does Net Buying Pressure Affect the Shape of Implied Volatility Functions written by Nicolas P. B. Bollen and published by . This book was released on 2012 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) of Samp;P 500 index options and options on twenty individual stocks. We find that time variation in the implied volatility of an option series is directly related to net buying pressure from public order flow. We also find that movements in implied volatility in the index option market are most strongly affected by buying pressure for index puts, while call options tend to dominate in stock option markets. Simulated delta-neutral trading strategies that sell options generate abnormal returns that match the deviations of the IVFs from historical volatility levels. Index option abnormal returns decrease monotonically across exercise prices and are significant, while stock option abnormal returns are symmetric, smaller, and insignificant. When vega risk is also hedged in the simulations using index options, however, the abnormal returns go from positive to negative, indicating that the steeply sloped IVF for index options does not present a profitable arbitrage opportunity once the costs of hedging have been considered.

Download or read book A Generalized Procedure for Building Trees for the Short Rate and Its Application to Determining Market Implied Volatility Functions written by John C. Hull and published by . This book was released on 2017 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate models can be accommodated. It shows how a piecewise linear volatility function can be calibrated to market data and, using market data from days during the period 2004 to 2013, finds that the best fit to cap prices is provided by a function remarkably similar to that estimated by Deguillaume et al (2013) from historical data.

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 Determinants of Implied Volatility Function on the Nifty Index Options Market written by Vijayakumar Narayanamoorthy and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we examine two important propositions for the Indian options market: (1) the relationship between implied volatility and moneyness referred to as volatility smile and (2) the potential determinants of the smile asymmetry. We use daily data for the S&P CNX Nifty index call and put options and the underlying market index for the calendar years 2004 and 2005. We find that the volatility functions exhibit a positive slope in the Indian context using alternative measures of moneyness, thus confirming the consistency of our findings. Our evidence on smile asymmetry is in contrast with findings for mature markets, which exhibit negative asymmetry profiles in general. This may be owing to differences in investors' behaviour and market microstructure between mature and emerging markets. We also show that historical volatility and time to expiration are the potential determinants of smile asymmetry in India, as is the case with international evidence. We feel that a strong theoretical foundation should be provided for this observable empirical phenomenon.

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