Download or read book Local Volatility from American Options written by Stefano De Marco and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we focus on short-time asymptotics for American options in the case of local and stochastic volatility models. As a by-product, we obtain an efficient algorithm for calibrating Dupire's local volatility to American options, starting from an arbitrage-free parametrization of a European implied volatility. This is illustrated by various numerical experiments.
Download or read book Fast and Reliable Pricing of American Options with Local Volatility written by and published by . This book was released on 2006 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Valuation of Barrier and American Options in Local Volatility Models with Jumps written by Bjorn Eriksson and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Options Under Stochastic Volatility written by Arun Chockalingam and published by . This book was released on 2012 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrates that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes. Option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on European options. We consider the problem of pricing American options under stochastic volatility which has relatively had much less attention from literature. First, we develop an exercise-policy improvement procedure to compute the optimal exercise policy and option price. We show that the scheme monotonically converges for various popular stochastic volatility models in literature. Second, using this computational tool, we explore a variety of questions that seek insights into the dependence of option prices, exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility.
Download or read book Essays on American Options Pricing Under Levy Models with Stochastic Volatility and Jumps written by Ye Chen and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In ``A Multi-demensional Transform for Pricing American Options Under Stochastic Volatility Models", we present a new transform-based approach for pricing American options under low-dimensional stochastic volatility models which can be used to construct multi-dimensional path-independent lattices for all low-dimensional stochastic volatility models given in the literature, including SV, SV2, SVJ, SV2J, and SVJ2 models. We demonstrate that the prices of European options obtained using the path-independent lattices converge rapidly to their true prices obtained using quasi-analytical solutions. Our transform-based approach is computationally more efficient than all other methods given in the literature for a large class of low-dimensional stochastic volatility models. In ``A Multi-demensional Transform for Pricing American Options Under Levy Models", We extend the multi-dimensional transform to Levy models with stochastic volatility and jumps in the underlying stock price process. Efficient path-independent tree can be constructed for both European and American options. Our path-independent lattice method can be applied to almost all Levy models in the literature, such as Merton (1976), Bates (1996, 2000, 2006), Pan (2002), the NIG model, the VG model and the CGMY model. The numerical results show that our method is extemly accurate and fast. In ``Empirical performance of Levy models for American Options", we investigate in-sample fitting and out-of-sample pricing performance on American call options under Levy models. The drawback of the BS model has been well documented in the literatures, such as negative skewness with excess kurtosis, fat tail, and non-normality. Therefore, many models have been proposed to resolve known issues associated the BS model. For example, to resolve volatility smile, local volatility, stochastic volatility, and diffusion with jumps have been considered in the literatures; to resolve non-normality, non-Markov processes have been considered, e.g., Poisson process, variance gamma process, and other type of Levy processes. One would ask: what is the gain from each of the generalized models? Or, which model is the best for option pricing? We address these problems by examining which model results in the lowest pricing error for American style contracts. For in-sample analysis, the rank (from best to worst) is Pan, CGMYsv, VGsv, Heston, CGMY, VG and BS. And for out-of-sample pricing performance, the rank (from best to worst) is CGMYsv, VGsv, Pan, Heston, BS, VG, and CGMY. Adding stochastic volatility and jump into a model improves American options pricing performance, but pure jump models are worse than the BS model in American options pricing. Our empirical results show that pure jump model are over-fitting, but not improve American options pricing when they are applied to out-of-sample data.
Download or read book The Volatility Surface written by Jim Gatheral and published by . This book was released on 2006 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Methods for Option Pricing written by Yves Achdou and published by SIAM. This book was released on 2005-01-01 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors review some important aspects of finance modeling involving partial differential equations and focus on numerical algorithms for the fast and accurate pricing of financial derivatives and for the calibration of parameters. This book explores the best numerical algorithms and discusses them in depth, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries.
Download or read book Fitting Local Volatility Analytic And Numerical Approaches In Black scholes And Local Variance Gamma Models written by Andrey Itkin and published by World Scientific. This book was released on 2020-01-22 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
Download or read book Emerging Financial Derivatives written by Jerome Yen and published by Routledge. This book was released on 2014-11-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exotic options and structured products are two of the most popular financial products over the past ten years and will soon become very important to the emerging markets, especially China. This book first discusses the products' recent development in the world and provides comprehensive overview of the major products. The book also discusses the risks of issuing and buying such products as well as the techniques to price them and to assess the risks. Volatility is the most important factor in determining the return and risk. Therefore, significant part of the book's content discusses how we can measure the volatility by using local and stochastic volatility models — Heston Model and Dupire Model, the volatility surface, the term structure of volatility, variance swaps, and breakeven volatility. The book introduces a set of dimensions which can be used to describe structured products to help readers to classify them. It also describes the more commonly traded exotic options with details. The book discusses key features of each exotic option which can be used to develop structured products and covers their pricing models and when to issue such products that contain such exotic options. This book contains several case studies about how to use the models or techniques to price and hedge risks. These case analyses are illuminating.
Download or read book American Option Pricing Under Stochastic Volatility written by Manisha Goswami and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximate method to price American options makes use of the fact that accurate pricing of these options does not require exact determination of the early exercise boundary. Thus, the procedure mixes the two models of constant and stochastic volatility. The idea is to obtain early exercise boundary through constant volatility model using the approximation methods of AitSahlia and Lai or Ju and then utilize this boundary to price the options under stochastic volatility models. The data on S & P 100 Index American options is used to analyze the pricing performance of the mixing of the two models. The performance is studied with respect to percentage pricing error and absolute pricing errors for each money-ness maturity group.
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research-including Risk magazine's 2013 Quant of the Year-Nonlinear Option Pricing compares various numerical methods for solving hi
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
Download or read book Foundations of Quantization for Probability Distributions written by Siegfried Graf and published by Springer. This book was released on 2007-05-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Download or read book Estimation of Volatilities Under a Merton s Jump diffusion Model and an Uncertain Volatility Model written by Changhong He and published by . This book was released on 2005 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods for Financial Markets written by Monique Jeanblanc and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.
Download or read book American Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter. This book was released on 2013-11-27 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
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.
