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 Interpreting the Volatility Smile written by Steven A. Weinberg and published by . This book was released on 2001 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Information Behind the Implied Volatility Smile written by Michele A. Kreisler and published by . This book was released on 1996 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smile in Motion written by Martin Wallmeier and published by . This book was released on 2012 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpreting the Volatility Smile written by Steven Aric Weinberg and published by . This book was released on 2003 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper evaluates how useful the information contained in options prices is for predicting future price movements of the underlying assets. We develop an improved semiparametric methodology for estimating risk-neutral probability density functions (PDFs), which allows for skewness and intertemporal variation in higher moments. We use this technique to estimate a daily time series of risk-neutral PDFs spanning the late 1980's through 1999, for Samp;P 500 futures, U.S. dollar/Japanese yen futures and U.S. dollar/deutsche mark futures, using options on these futures. For the foreign exchange futures, we find little discernable additional information contained in the estimated PDFs beyond the information derived from the Black-Scholes model, a fully parametric specification. For Samp;P 500 futures, we find that the risk-neutral distribution implied by the volatility smile better fits the realized returns than the Black-Scholes model, although this better overall fit is not exhibited in the second and third moments.
Download or read book The Impact of Computational Error on the Volatility Smile written by Don M. Chance and published by . This book was released on 2013 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well-known that the market prices of options produce implied volatilities that inexplicably vary by exercise price in a pattern often referred to as the volatility smile. This paper shows that not only do market prices produce volatility smiles, but so do model prices. This result occurs because of root finding algorithms, tolerance assumptions, numerical precisions, and quotation finiteness. Moreover, some assumptions result in patterns that resemble the smirks, and skews sometimes observed in market data. Consistent with empirical observations, the effects are greater the shorter the expiration. Elimination of these patterns is virtually impossible on a practical level, and even second-best results can be obtained only if options are traded with quadruple precision pricing and machine precision tolerance is assumed. We conclude that while alternative explanations for the smile can be true, prices generated under perfect conditions cannot even eliminate these smile, smirk, and skew patterns.
Download or read book The Slope of the Smile and the Comovement of Volatility and Returns written by Anthony Neuberger and published by . This book was released on 2009 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: The slope of the implied volatility smile reflects the correlation between volatility shocks and returns. By defining the slope as the difference between two implied variances, the relationship between the slope, and the correlation between volatility and returns can be derived formally in a way that is essentially model free. More specifically, the slope is the price of a swap contract where the floating leg is the covariation between returns on the underlying asset and changes in its volatility. The term structure of the slope carries information about the correlation between returns and future volatility. The results are analogous to the finding that the model free implied variance is equal to the expected realized variance under the pricing measure.
Download or read book Deconstructing the Volatility Smile written by Romano Trabalzini and published by . This book was released on 2014 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the relationship between the implied volatility smile and the underlying joint density of two quantities characterizing the stochastic volatility process - namely the mean integrated variance, $ frac{1}{T} int_0^T sigma_s^2ds$, and the stochastic integral $ int_0^T sigma_s dW_{s}^{ sigma}$. A simple form of this joint density is proposed which, when fit to the zero correlation smile and a single non-zero correlation smile, will then generate to good agreement the smile for an arbitrarily chosen correlation. Further, the method complements and extends the work of cite{carr_lee_robust} and cite{friz_gatheral} to non-zero correlation. In doing so, it allows for the study of volatility derivatives in the quanto case which is particularly relevant in the foreign exchange markets.
Download or read book The Implied Volatility Bias and Option Smile written by Kanlaya Jintanakul Barr and published by . This book was released on 2009 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling the Implied Volatility Smile written by Kim Sundkvist and published by . This book was released on 2000 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Equity Volatility Smile and Default Risk written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the theoretical prediction, increasing default risk leads to an increasing steepness of the monotonically downward sloping stock option smile. However, extant empirical evidence of this prediction is extremely rare and limited to the slope of the smile at the ATM strike level. The empirical analysis of 23 DAX companies during a 3 year period showed the following: The effect of increasing default risk on the smile can be decomposed into a default-risk-only effect on the one hand and a volatility-only effect on the other. The default-risk-only effect is the impact of rising default risk on the smile if the level of equity volatility is kept constant, while the volatility-only effect designates the impact of increasing equity volatility on the smile, if the level of default risk is kept unchanged. The default-risk-only effect leads to increasing steepness of both wings of the U-shaped smile, whereas the volatility-only effect entails a flattening and right-translation of the smile. Both effects together finally imply a flattening and right-translation of the smile.
Download or read book The Volatility Surface written by Jim Gatheral and published by Wiley. This book was released on 2006-09-18 with total page 208 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 Volatility Smile Dynamics in Scenario Analysis written by Kim Sundkvist and published by . This book was released on 2000 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Volatility Smile as Relativistic Effect written by Zura Kakushadze and published by . This book was released on 2017 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black-Scholes-Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no "speed limit" and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Levy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.
Download or read book Determinants of Implied Volatility Smiles An Empirical Analysis Using Intraday DAX Equity Options written by Andreas Rathgeber and published by . This book was released on 2018 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: By extending and reviewing determinants of the implied volatility in the context of high frequency (HF) trade-by-trade DAX equity options from the EUREX a mean-reversion autocorrelation process is revealed, besides confirming low frequency results such as moneyness, time, liquidity, volume and underlying moment dependencies. Furthermore, we show, that the mean-reversion process is present, even if we control for fluctuating trades between bid and ask prices. It is induced by algorithmic market making and market microstructure effects. We address the HF research gap in market microstructure literature expressed by O'Hara (2015), who argues that markets and trading is radically different today, which consequently altered the basic constructs of market microstructure, and we give additional explanation for the flickering quote hypothesis of Hasbrouck and Saar (2009).
Download or read book Of Smiles and Smirks written by Sanjiv Ranjan Das and published by . This book was released on 2015 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical anamolies in the Black-Scholes model have been widely documented in the Finance literature. Patterns in these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities) have also been widely documented. Theoretical efforts in the literature at addressing these anamolies have largely centered around extensions of the basic Black-Scholes model. Two approaches have become especially popular in this context -- introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonly-used versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We focus especially on the possible quot;term-structuresquot;: of skewness, kurtosis, and the implied volatility smile that can arise under each model. Our central finding is that each model exhibits moment patterns and implied volatility smiles that are consistent with some of the observed anamolies, but not with others. In sum, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.
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.
