Download or read book An Empirical Study of the Dynamics of Implied Volatility Indices written by Bujar Huskaj and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper compares the empirical performance of continuous time models for the dynamics of nine different implied volatility indices. The models include linear, quadratic and nonlinear drift specifications with affine, constant elasticity of variance (CEV) and stochastic elasticity of variance (SEV) diffusion parts. We find that a nonlinear drift specification is important when imposing an affine structure on the diffusion, whereas a simple linear drift is adequate with a CEV and SEV specification, of which the SEV is dominant. For all but two of the indices we investigate, the best specification is a SEV diffusion with linear drift. For gold and the USD/EUR exchange rate there is little difference between a CEV and SEV diffusion with linear drift.

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 Dynamics of Implied Volatility Surfaces written by Rama Cont and published by . This book was released on 2002 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Empirical Comparison of Continuous Time Models of Implied Volatility Indices written by George Dotsis and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We explore the ability of alternative popular continuous-time diffusion and jump diffusion processes to capture the dynamics of implied volatility indices over time. The performance of the various models is assessed under both econometric and financial metrics. To this end, data are employed from major European and American implied volatility indices and the rapidly growing CBOE volatility futures market. We find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics. Mean reversion is of second order importance though. The results are consistent across the various metrics, markets, and construction methodologies.

Download or read book Empirical Studies on Volatility in International Stock Markets written by Eugenie M.J.H. Hol and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Studies on Volatility in International Stock Markets describes the existing techniques for the measurement and estimation of volatility in international stock markets with emphasis on the SV model and its empirical application. Eugenie Hol develops various extensions of the SV model, which allow for additional variables in both the mean and the variance equation. In addition, the forecasting performance of SV models is compared not only to that of the well-established GARCH model but also to implied volatility and so-called realised volatility models which are based on intraday volatility measures. The intended readers are financial professionals who seek to obtain more accurate volatility forecasts and wish to gain insight about state-of-the-art volatility modelling techniques and their empirical value, and academic researchers and students who are interested in financial market volatility and want to obtain an updated overview of the various methods available in this area.

Download or read book The Dynamics of the S P 500 Implied Volatility Surface written by George S. Skiadopoulos and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This empirical study is motivated by the literature on quot;smile-consistentquot; arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a quot;Procrustesquot; type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing.

Download or read book Dynamics of the Implied Volatility Term Structure written by Arnaud Wolf and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Information Content of Implied Volatility an Empirical Study of the FTSE 100 Stock Index Options written by Charalambos Vovos and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Empirical Study on the Implied Volatility of FTSE 100 Index Options written by Yue Liu and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Predictable Dynamics in the S P 500 Index Options Implied Volatility Surface written by Sílvia Gonçalves and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper, we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the Samp;P 500 index options IVS. In the first stage, we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas, et. al., (1998). In the second-stage, we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models. We find that not only the Samp;P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic significance of this statistical predictability with mixed findings. Whereas profitable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this profitability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying Samp;P 500 implied volatility surface may be not inconsistent with market efficiency.

Download or read book On the Dynamics and Information Content of Implied Volatility written by Bent Jesper Christensen and published by . This book was released on 2008 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new research design is introduced for the empirical analysis of the relationship between implied volatility and ex-post realized volatility. The dynamics of volatility are emphasized, and the analysis is cast in terms of non-overlapping data, so that exactly one implied and one realized volatility estimate pertain to each period under consideration. The conclusions from the empirical analysis when using our design are significantly different from those previously reached. Recent literature indicates that implied volatility contains little information about future volatility, beyond that contained in the history of realized volatility. We show that on the contrary, implied volatility efficiently predicts future realized volatility and in particular subsumes the information content of past realized volatility.

Download or read book The Volatility Smile written by Emanuel Derman and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Predictable Dynamics in the S P 500 Index Options Implied Volatility Surface written by Silvia Goncalves and published by . This book was released on 2005 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Empirical Research of Asymmetry and Forecast Errors in the Implied Volatility Index written by Chi-Tai Lin and published by . This book was released on 2010 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Implied Volatility and Stock Market Speculation written by Ramesh Thimmaraya and published by . This book was released on 2017 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability of an economy is directly linked to the stability of the capital markets in which it operates and vice versa. The capital market stability is in turn linked to the asset price dynamics; most of these asset prices are modelled based on expected rate of return. The expected rate of return and direction of markets is determined from the implied market volatility (VIX index). The implied volatility is a forward looking variable which tells about the realised market volatility based of market participant's expectations. Most of the times this implied volatility is over estimated compared to the realised volatility due to the speculative behaviour of the market participants. This speculative behaviour causes virtual dynamics in the implied variables which in turn caused virtual dynamics in the individual asset prices. The virtual dynamics in the asset prices causes the divergence in the realised or fundamental value of the market; which can be attributed to the irrational behavioural of the financial market participants. The present paper aims at understanding the source and level of the speculation, and also an attempt has been made to develop a novel quantitative behavioral framework to understand and rectify this speculative behaviour. An empirical analysis has been carried out on the S&P 500 Index and CBOE VIX Index to validate the proposed model. Some interesting results have been obtained from the present study which clearly shows the quantitative behavioural model has the capability to convergence the expected volatility with the realised market volatility, this helps the market participants, regulators and policy makers to make necessary corrections based on the predicted speculation.

Download or read book Construction and Interpretation of Model free Implied Volatility written by Torben G. Andersen and published by . This book was released on 2007 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the VIX index is computed through a tail-truncation which renders it more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and hence estimate the corresponding volatility measures, under the standard Black-Scholes model. Finally, we undertake the first empirical exploration of the CIV measures in the literature. Our results indicate that the measure can help us refine and systematize the information embedded in the derivatives markets. As such, the CIV measure may serve as a tool to facilitate empirical analysis of both volatility forecasting and volatility risk pricing across distinct future states of the world for diverse asset categories and time horizons.

Download or read book Volatility and Correlation written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2005-07-08 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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