Upper Bounds For American Options

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Upper Bounds for American Options

Author : Mo Chaudhury
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Upper Bounds for American Options by : Mo Chaudhury

Download or read book Upper Bounds for American Options written by Mo Chaudhury and published by . This book was released on 2003 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a fuller characterization of the analytical upper bounds for American options than has been available to date. We establish properties required of analytical upper bounds without any direct reliance on the exercise boundary. A class of generalized European claims on the same underlying asset is then proposed as upper bounds. This set contains the existing closed form bounds of Margrabe (1978) and Chen and Yeh (2002) as special cases and allows randomization of the maturity payoff. Due to the European nature of the bounds, across-strike arbitrage conditions on option prices seem to carry over to the bounds. Among other things, European option spreads may be viewed as ratio positions on the early exercise option. To tighten the upper bound, we propose a quasi-bound that holds as an upper bound for most situations of interest and seems to offer considerable improvement over the currently available closed form bounds. As an approximation, the discounted value of Chen and Yeh's (2001) bound holds some promise. We also discuss implications for parametric and nonparametric empirical option pricing. Sample option quotes for the European (XEO) and the American (OEX) options on the Samp;P 100 Index appear well behaved with respect to the upper bound properties but the bid-ask spreads are too wide to permit a synthetic short position in the early exercise option.

New Bounds on American Option Prices

Author : In Joon Kim
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis New Bounds on American Option Prices by : In Joon Kim

Download or read book New Bounds on American Option Prices written by In Joon Kim and published by . This book was released on 2007 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we develop new upper and lower bounds on American option prices which improve the bounds by Broadie and Detemple. The main idea is the consideration of doubly capped call options which have two cap prices. We present a new option price approximation based on the two upper bounds. On average, our upper bound extrapolation (named UBE) has an average accuracy better than a 1,000 time-step binomial tree with a computation speed comparable to a 100 time-step binomial tree. We also provide a new method of approximating the optimal exercise boundaries of American options.

Robust Upper Bounds for American Put Options

Author : Ye Du
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Robust Upper Bounds for American Put Options by : Ye Du

Download or read book Robust Upper Bounds for American Put Options written by Ye Du and published by . This book was released on 2017 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop robust and model-free upper bounds for American put option prices. Our bounds have all of those appealing features of the upper bounds for European options provided in DeMarzo et al. (2016) but cover much more popular derivatives in practice. Numerical results demonstrate that our results are empirically meaningful.

Pricing American Options

Author : Leonid Kogan
Publisher : Forgotten Books
ISBN 13 : 9780666532459
Total Pages : 82 pages
Book Rating : 4.5/5 (324 download)

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Book Synopsis Pricing American Options by : Leonid Kogan

Download or read book Pricing American Options written by Leonid Kogan and published by Forgotten Books. This book was released on 2018-02-27 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Pricing American Options: A Duality Approach The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. In addition, we explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is obtained by simulating a different stochastic process that is determined by choosing an appropriate supermartingale. We justify this procedure by representing the American option price as a solution of a dual minimization problem, which is the main theoretical result of this paper. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Bounds on the American Option

Author : Anthony Neuberger
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Bounds on the American Option by : Anthony Neuberger

Download or read book Bounds on the American Option written by Anthony Neuberger and published by . This book was released on 2007 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential feature of American style claims lies in the holder's right to time the exercise decision. The value of the claim depends on the information about future prices that the holder will acquire over time. Much of the literature makes restrictive assumptions about information revelation - for example that the underlying price process is Markov. This paper explores the upper bound on the price of an American option, placing no assumptions on the information structure. The analysis provides insight into the processes that make the American feature valuable, and points the way to hedging strategies for American options that are robust to model error.

American Option Valuation

Author : Jerome Detemple
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis American Option Valuation by : Jerome Detemple

Download or read book American Option Valuation written by Jerome Detemple and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop lower and upper bounds on the prices of American call and put options written on a dividend paying asset. We provide two option price approximations, one based on the lower bound (term LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a 1000-step binomial tree with a computation speed comparable to a 50-step binomial tree. We introduce a modification of the binomial method (termed BBSR) which is very simple to implement and performs remarkably well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices.

Mathematical Models of Financial Derivatives

Author : Yue-Kuen Kwok
Publisher : Springer Science & Business Media
ISBN 13 : 3540686886
Total Pages : 541 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Mathematical Models of Financial Derivatives by : Yue-Kuen Kwok

Download or read book Mathematical Models of Financial Derivatives written by Yue-Kuen Kwok and published by Springer Science & Business Media. This book was released on 2008-07-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes)

Author : Cheng Few Lee
Publisher : World Scientific
ISBN 13 : 9811202400
Total Pages : 5053 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes) by : Cheng Few Lee

Download or read book Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes) written by Cheng Few Lee and published by World Scientific. This book was released on 2020-07-30 with total page 5053 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Optimal Stopping and Free-Boundary Problems

Author : Goran Peskir
Publisher : Springer Science & Business Media
ISBN 13 : 3764373903
Total Pages : 515 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Optimal Stopping and Free-Boundary Problems by : Goran Peskir

Download or read book Optimal Stopping and Free-Boundary Problems written by Goran Peskir and published by Springer Science & Business Media. This book was released on 2006-11-10 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

The Concepts and Practice of Mathematical Finance

Author : Mark Suresh Joshi
Publisher : Cambridge University Press
ISBN 13 : 9780521823555
Total Pages : 496 pages
Book Rating : 4.8/5 (235 download)

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Book Synopsis The Concepts and Practice of Mathematical Finance by : Mark Suresh Joshi

Download or read book The Concepts and Practice of Mathematical Finance written by Mark Suresh Joshi and published by Cambridge University Press. This book was released on 2003-12-24 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: For those starting out as practitioners of mathematical finance, this is an ideal introduction. It provides the reader with a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Uniquely, the book includes extensive discussion of the ideas behind the models, and is even-handed in examining various approaches to the subject. Thus each pricing problem is solved using several methods. Worked examples and exercises, with answers, are provided in plenty, and computer projects are given for many problems. The author brings to this book a blend of practical experience and rigorous mathematical background, and supplies here the working knowledge needed to become a good quantitative analyst.

Pricing American Options

Author : Leonid Kogan
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (58 download)

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Book Synopsis Pricing American Options by : Leonid Kogan

Download or read book Pricing American Options written by Leonid Kogan and published by . This book was released on 2001 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest. Keywords: Asset pricing, dynamic programming, simulation, American option, optimal stopping, duality.

American-Type Options

Author : Dmitrii S. Silvestrov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110329840
Total Pages : 572 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis American-Type Options by : Dmitrii S. Silvestrov

Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-12-17 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods 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 volume presents 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.

A Monte Carlo Method for Pricing American Options

Author : Diego Garcia
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (34 download)

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Book Synopsis A Monte Carlo Method for Pricing American Options by : Diego Garcia

Download or read book A Monte Carlo Method for Pricing American Options written by Diego Garcia and published by . This book was released on 1999 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytical upper bounds for american option prices

Author : 葉仕國
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (848 download)

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Book Synopsis Analytical upper bounds for american option prices by : 葉仕國

Download or read book Analytical upper bounds for american option prices written by 葉仕國 and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematics of Derivatives Securities with Applications in MATLAB

Author : Mario Cerrato
Publisher : John Wiley & Sons
ISBN 13 : 1119973414
Total Pages : 201 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis The Mathematics of Derivatives Securities with Applications in MATLAB by : Mario Cerrato

Download or read book The Mathematics of Derivatives Securities with Applications in MATLAB written by Mario Cerrato and published by John Wiley & Sons. This book was released on 2012-02-24 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.

American Put Options

Author : Donna Salopek
Publisher : CRC Press
ISBN 13 : 9780582315945
Total Pages : 132 pages
Book Rating : 4.3/5 (159 download)

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Book Synopsis American Put Options by : Donna Salopek

Download or read book American Put Options written by Donna Salopek and published by CRC Press. This book was released on 1997-03-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computational approaches.

Derivatives and Risk Management:

Author : Madhumathi
Publisher : Pearson Education India
ISBN 13 : 9332506817
Total Pages : 542 pages
Book Rating : 4.3/5 (325 download)

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Book Synopsis Derivatives and Risk Management: by : Madhumathi

Download or read book Derivatives and Risk Management: written by Madhumathi and published by Pearson Education India. This book was released on 2011 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the incorporation of real-life examples from Indian organizations, Derivatives and Risk Management provides cutting-edge material comprising new and unique study tools and fresh, thought-provoking content. The organization of the text is designed to conceptually link a firm’s actions to its value as determined in the derivatives market. It addresses the specific needs of Indian students and managers by successfully blending the best global derivatives and risk management practices with an in-depth coverage of the Indian environment.