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Semiparametric Modeling Of Implied Volatility
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Book Synopsis Semiparametric Modeling of Implied Volatility by : Matthias R. Fengler
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.
Book Synopsis A Semiparametric Factor Model for Implied Volatility Surface Dynamics by : Matthias R. Fengler
Download or read book A Semiparametric Factor Model for Implied Volatility Surface Dynamics written by Matthias R. Fengler and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.
Book Synopsis A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics by : Matthias R. Fengler
Download or read book A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics written by Matthias R. Fengler and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics by : Matthias R. Fengler
Download or read book A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics written by Matthias R. Fengler and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.
Book Synopsis Semi-parametric Implied Volatility Surface Models and Forecasts Based on a Regression Tree-boosting Algorithm by :
Download or read book Semi-parametric Implied Volatility Surface Models and Forecasts Based on a Regression Tree-boosting Algorithm written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new methodology for semi-parametric modelling of implied volatility surfaces is presented. This methodology is dependent upon the development of a feasible estimating strategy in a statistical learning framework. Given a reasonable starting model, a boosting algorithm based on regression trees sequentially minimizes generalized residuals computed as differences between observed and estimated implied volatilities. To overcome the poor predicting power of existing models, a grid is included in the region of interest and a cross-validation strategy is implemented to find an optimal stopping value for the boosting procedure. Back testing the out-of-sample performance on a large data set of implied volatilities from S & P 500 options provides empirical evidence of the strong predictive power of the model. Accurate IVS forecasts also for single equity options assist in obtaining reliable trading signals for very profitable pure option trading strategies.
Book Synopsis Handbook of Volatility Models and Their Applications by : Luc Bauwens
Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-03-22 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
Book Synopsis VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings by : Ralf Brüggemann
Download or read book VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings written by Ralf Brüggemann and published by . This book was released on 2017 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading times series using the vector autoregressive (VAR) framework and analyzes associated movements of these factors with movements in some macroeconomic variables of the Euro-economy.
Book Synopsis Implicit Volatilities by : Robert Schott
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 [...]
Book Synopsis Analytically Tractable Stochastic Stock Price Models by : Archil Gulisashvili
Download or read book Analytically Tractable Stochastic Stock Price Models written by Archil Gulisashvili and published by Springer Science & Business Media. This book was released on 2012-09-04 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.
Book Synopsis Handbook of Computational Finance by : Jin-Chuan Duan
Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Book Synopsis Paris-Princeton Lectures on Mathematical Finance 2004 by : René Carmona
Download or read book Paris-Princeton Lectures on Mathematical Finance 2004 written by René Carmona and published by Springer. This book was released on 2007-08-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by René Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyên Pham.
Book Synopsis VAR Modeling for Dynamic Loadings Driving Volatility Strings by : Ralf Brüggemann
Download or read book VAR Modeling for Dynamic Loadings Driving Volatility Strings written by Ralf Brüggemann and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading time series using the vector autoregressive (VAR) framework and analyzes the dynamic relationship of these factors with economic indicators.
Book Synopsis A Semiparametric Estimation of Liquidity Effects on Option Pricing by : Eva Ferreira
Download or read book A Semiparametric Estimation of Liquidity Effects on Option Pricing written by Eva Ferreira and published by . This book was released on 1999 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Chaos Expansions in Finance by : David Nicolay
Download or read book Asymptotic Chaos Expansions in Finance written by David Nicolay and published by Springer. This book was released on 2014-11-25 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.
Book Synopsis Modelling and Forecasting Realized Volatility with Semiparametric Diffusion Models by : Maxim Fedotov
Download or read book Modelling and Forecasting Realized Volatility with Semiparametric Diffusion Models written by Maxim Fedotov and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis deals with application of semiparametric diffusion models for Realized Variance process. Theoretical foundations of the work are based on two papers: Ait-Sahalia 1995 who introduced semiparametric modeling for interest rate processes and its applications for derivatives pricing and Koo and Linton 2012 who relaxed assumption of stationarity of the process and introduced more flexibility into the model and its estimation. The thesis has two main goals - first, try to apply semiparametric diffusion models on Realized Variance time series, emerged recently thanks to high- frequency trading and gaining attention from many researchers today. This includes estimation of the model and behavior of the estimates with time and state. Second, in this thesis we are going beyond purely analytical applications of estimated model by trying to build simulations framework around it and in particular study performance of risk forcast in this framework. This, infact, is the first attempt to use this framework for forecasting Realized Variance series, in general, and by utilizing simulations, in particular. It is established in the thesis that the estimation of the process parameters gives results in line with expectations and these results indeed appear to capture true observed dynamics of the process. However, though some of the results look promising, in the course of numerical part of the thesis, a number of complications revealed themselves, which in this work were attempted to be addressed in a simplified fashion, and, undoubtedly, form an interesting direction for further research.
Book Synopsis Statistics of Financial Markets by : Jürgen Franke
Download or read book Statistics of Financial Markets written by Jürgen Franke and published by Springer Science & Business Media. This book was released on 2010-11-22 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics of Financial Markets offers a vivid yet concise introduction to the growing field of statistical application in finance. The reader will learn the basic methods of evaluating option contracts, analysing financial time series, selecting portfolios and managing risks making realistic assumptions of the market behaviour. The focus is both on the fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, thus making the book the ideal basis for lecturers, seminars and crash courses on the topic. For the third edition the book has been updated and extensively revised. Several new aspects have been included: new chapters on long memory models, copulae and CDO valuation. Practical exercises have been added, the solutions of which are provided in the book by S. Borak, W. Härdle and B. Lopez Cabrera (2010) ISBN 978-3-642-11133-4. “Both R and Matlab Code, together with the data, can be downloaded by clicking on the Additional Information tab labeled “R and Matlab Code,” which you will find on the right-hand side of the webpage.”
Book Synopsis Analytical Methods in Statistics by : Matúš Maciak
Download or read book Analytical Methods in Statistics written by Matúš Maciak and published by Springer Nature. This book was released on 2020-07-19 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects peer-reviewed contributions on modern statistical methods and topics, stemming from the third workshop on Analytical Methods in Statistics, AMISTAT 2019, held in Liberec, Czech Republic, on September 16-19, 2019. Real-life problems demand statistical solutions, which in turn require new and profound mathematical methods. As such, the book is not only a collection of solved problems but also a source of new methods and their practical extensions. The authoritative contributions focus on analytical methods in statistics, asymptotics, estimation and Fisher information, robustness, stochastic models and inequalities, and other related fields; further, they address e.g. average autoregression quantiles, neural networks, weighted empirical minimum distance estimators, implied volatility surface estimation, the Grenander estimator, non-Gaussian component analysis, meta learning, and high-dimensional errors-in-variables models.
