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Quanto Implied Volatility Smile
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Book Synopsis Quanto Implied Volatility Smile by : Alessandro Cesarini
Download or read book Quanto Implied Volatility Smile written by Alessandro Cesarini and published by . This book was released on 2014 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a numerical procedure, addressed as copula integration method, to calculate quanto implied volatility adjustments. The method consists in a direct integration of the quanto vanilla payoff, using the bivariate terminal probability distribution of the asset and the relevant foreign exchange rate. The bivariate terminal distribution is obtained by coupling the marginal distributions of the two underlyings by means of a Gaussian copula. The asset and the foreign exchange rate marginal distributions are directly inferred from the corresponding Black-Scholes market volatility smiles. In order to obtain well defined marginal distributions, we propose an extrapolation method for the standard implied volatility outside the quoted region, which does not allow arbitrage opportunities. The validity of the copula integration method is established by comparing its predictions to exact results for quanto option prices, obtained by numerical computations in two realistic test cases, in which the dynamics of the assets is driven by a local volatility and a Heston stochastic volatility model.
Book Synopsis Information Behind the Implied Volatility Smile by : Michele A. Kreisler
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:
Book Synopsis Deconstructing the Volatility Smile by : Romano Trabalzini
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.
Book Synopsis The Volatility Smile by : Emanuel Derman
Download or read book The Volatility Smile written by Emanuel Derman and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options 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"--
Book Synopsis Quanto Pricing with Copulas by : Michael N. Bennett
Download or read book Quanto Pricing with Copulas written by Michael N. Bennett and published by . This book was released on 2003 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the practical problem of pricing a particular multi-asset option, a quanto FX option. The Black model, which corresponds to a jointly lognormal distribution of asset prices at expiry, is inconsistent with the implied volatility smile for each of the three relevant currency pairs. We demonstrate a practical methodology for constructing a model for the joint distribution that is calibrated to all relevant implied volatilities. The margins of this distribution are determined separately in an initial stage. To calibrate the joint distribution to the implied volatility smile on the remaining FX rate, we perturb the dependence structure associated with the Black model (the Normal copula) in order to influence the tail dependence characteristics of the resulting joint distribution.We calibrate our model to a number of real-life scenarios corresponding to several maturities and currency set-ups. We find that a well-known ad-hoc adjustment to the Black pricing formula often gives lower quanto call prices than those calculated under our transformed copula model. The relative difference in quanto prices with strikes furthest away from at-the-money is occasionally large (10-15%).
Book Synopsis Modeling the Implied Volatility Smile by : Kim Sundkvist
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:
Book Synopsis FX Options and Smile Risk by : Antonio Castagna
Download or read book FX Options and Smile Risk written by Antonio Castagna and published by John Wiley & Sons. This book was released on 2010-02-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The FX options market represents one of the most liquid and strongly competitive markets in the world, and features many technical subtleties that can seriously harm the uninformed and unaware trader. This book is a unique guide to running an FX options book from the market maker perspective. Striking a balance between mathematical rigour and market practice and written by experienced practitioner Antonio Castagna, the book shows readers how to correctly build an entire volatility surface from the market prices of the main structures. Starting with the basic conventions related to the main FX deals and the basic traded structures of FX options, the book gradually introduces the main tools to cope with the FX volatility risk. It then goes on to review the main concepts of option pricing theory and their application within a Black-Scholes economy and a stochastic volatility environment. The book also introduces models that can be implemented to price and manage FX options before examining the effects of volatility on the profits and losses arising from the hedging activity. Coverage includes: how the Black-Scholes model is used in professional trading activity the most suitable stochastic volatility models sources of profit and loss from the Delta and volatility hedging activity fundamental concepts of smile hedging major market approaches and variations of the Vanna-Volga method volatility-related Greeks in the Black-Scholes model pricing of plain vanilla options, digital options, barrier options and the less well known exotic options tools for monitoring the main risks of an FX options’ book The book is accompanied by a CD Rom featuring models in VBA, demonstrating many of the approaches described in the book.
Book Synopsis The Impact of Computational Error on the Volatility Smile by : Don M. Chance
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.
Book Synopsis The Slope of the Smile, and the Comovement of Volatility and Returns by : Anthony Neuberger
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.
Book Synopsis Smile in Motion by : Martin Wallmeier
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:
Book Synopsis On the Implied Volatility Layers Under the Future Risk-Free Rate Uncertainty by : Lin-Yee Hin
Download or read book On the Implied Volatility Layers Under the Future Risk-Free Rate Uncertainty written by Lin-Yee Hin and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper suggests a method of estimation of the implied volatility smile uncertainty of the observed options prices due to future risk-free rate uncertainty. The purpose is to quantify the range of uncertainty under different scenarios.We consider the setting where both the implied volatility and the risk free rate are calculated jointly from the observed option prices. Due to the cumulative risk-free rate uncertainty, the corresponding system of equations is underdetermined, leading to uncertainty in the volatility surface.We estimate the size of implied volatility layers between the surfaces representing the upper and lower bounds for the implied volatilities for the future risk-free rate uncertainty, defined by current Libor rate and the size of fluctuation estimated from the historical data.
Book Synopsis Trading Volatility by : Colin Bennett
Download or read book Trading Volatility written by Colin Bennett and published by . This book was released on 2014-08-17 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. "A master piece to learn in a nutshell all the essentials about volatility with a practical and lively approach. A must read!" Carole Bernard, Equity Derivatives Specialist at Bloomberg "This book could be seen as the 'volatility bible'!" Markus-Alexander Flesch, Head of Sales & Marketing at Eurex "I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money" Paul Stephens, Head of Institutional Marketing at CBOE "One of the best resources out there for the volatility community" Paul Britton, CEO and Founder of Capstone Investment Advisors "Colin has managed to convey often complex derivative and volatility concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject" Edmund Shing PhD, former Proprietary Trader at BNP Paribas "In a crowded space, Colin has supplied a useful and concise guide" Gary Delany, Director Europe at the Options Industry Council
Book Synopsis Exploring the Role of the Realized Return Distribution in the Formation of the Implied Volatility Smile by : George Chalamandaris
Download or read book Exploring the Role of the Realized Return Distribution in the Formation of the Implied Volatility Smile written by George Chalamandaris and published by . This book was released on 2017 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article explores the role of the realized return distribution in the formation of the observed implied volatility smile using the framework of an adaptive expectations model. According to this framework investors update their expectations of future events, through which options are priced, by incorporating information from the underlying asset traded in the spot market. Our study is conducted at the level of cumulants which provide a complete description of investors expectations and can be considered as largely non-parametric with a minimal set of assumptions for the stochastic process that drives asset returns. The empirical results, based on the S&P 500 index, support the significance of the realized distribution in the formation of the implied volatility smile.
Book Synopsis Understanding Risk by : David Murphy
Download or read book Understanding Risk written by David Murphy and published by CRC Press. This book was released on 2008-04-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sound risk management often involves a combination of both mathematical and practical aspects. Taking this into account, Understanding Risk: The Theory and Practice of Financial Risk Management explains how to understand financial risk and how the severity and frequency of losses can be controlled. It combines a quantitative approach with a
Book Synopsis Quadratic Volatility Smiles by : Haim Reisman
Download or read book Quadratic Volatility Smiles written by Haim Reisman and published by . This book was released on 2001 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper assumes that the implied volatility of options with some given expiration is a quadratic function of the moneyness. The coefficients of this quadratic function (the smile) are time dependent and stochastic. The paper derives exposure parameters of the price of the option to the local change in each of the smile coefficients, and an approximate formula for their risk adjusted expected value. These are important in managing the exposure of the price of an option portfolio to changes in the smile coefficients.
Book Synopsis Of Smiles and Smirks by : Sanjiv Ranjan Das
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.
Book Synopsis Implied Volatility Smiles by : Bernard Dumas
Download or read book Implied Volatility Smiles written by Bernard Dumas and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Implied volatility quot;smilesquot; have been documented in a number of option markets worldwide. The volatilities implied by the Black-Scholes (1973) model tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) offer an explanation for this behavior, that is, the volatility of the return of the underlying asset is a deterministic function of the asset price level and time. Their option valuation methodology, dubbed the quot;implied binomial treequot; approach, describes (perfectly) the observed structure of options prices and purportedly provides more accurate hedge ratios. We systematically evaluate the empirical properties of the implied binomial tree approach to option valuation using Samp;P 500 index options during the period June 1988 and December 1993.
