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American Option Pricing And Exercising With Transaction Costs
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Book Synopsis American Option Pricing and Exercising with Transaction Costs by : Valeriy Zakamulin
Download or read book American Option Pricing and Exercising with Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2010 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal transaction policy of the option holder. We examine the effects on the reservation option prices and the corresponding exercise policies of varying the levels of absolute risk aversion and transaction costs.
Book Synopsis Do Transaction Costs Affect the Optimal Exercise Strategy for American Put Options? by : Norman Seeger
Download or read book Do Transaction Costs Affect the Optimal Exercise Strategy for American Put Options? written by Norman Seeger and published by . This book was released on 2012 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we theoretically analyze the effect of proportional transaction costs in the underlying on the optimal exercise strategy for American put options. Interestingly the results offer a theoretical explanation above other results in the literature for two types of empirically observed (irrational) investor's behavior; quot;faulty exercisequot; (option is exercised when not optimal) and quot;failure to exercisequot; (option is not exercised, although it is optimal). We show that for determining the exercise strategy in the presence of proportion transaction costs it becomes crucial important that (a) actually the holder of the option is in charge to decide about exercising or not, and that (b) it is important according to which investment strategy the investor is holding the option. Using a model which explicitly takes proportional transaction costs into account, we show for a realistic parameterization that, conditional on the investor's investment strategy, it maybe optimal to postpone exercising of put options, or to exercise more often compared to the standard frictionless theory. We also quantify that an investor neglecting transaction costs when determining the exercise strategy will make considerable pricing errors.
Download or read book Options written by Robert W. Kolb and published by Prentice Hall. This book was released on 1991 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Options: The Investor's Complete Toolkit covers the qualitative aspects of options most visible to the public -- profit motivated trading. And, it goes much further -- highlighting the quantitative side of options for portfolio managers, risk managers, hedging strategists, financial engineers, and arbitrageurs.
Book Synopsis The Numerical Solution of the American Option Pricing Problem by : Carl Chiarella
Download or read book The Numerical Solution of the American Option Pricing Problem written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Book Synopsis Valuation, Empirical Analysis, and Optimal Exercise of Open-End Turbo Certificates by : Sebastian Paik
Download or read book Valuation, Empirical Analysis, and Optimal Exercise of Open-End Turbo Certificates written by Sebastian Paik and published by University of Bamberg Press. This book was released on 2014 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Derivative Pricing in Discrete Time by : Nigel J. Cutland
Download or read book Derivative Pricing in Discrete Time written by Nigel J. Cutland and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.
Book Synopsis Nonlinear Option Pricing by : Julien Guyon
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.
Book Synopsis Option Pricing by : Menachem Brenner
Download or read book Option Pricing written by Menachem Brenner and published by Free Press. This book was released on 1983 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Basic Black-Scholes: Option Pricing and Trading by : Timothy Falcon Crack
Download or read book Basic Black-Scholes: Option Pricing and Trading written by Timothy Falcon Crack and published by Timothy Crack. This book was released on 2022-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Note: eBook now available; see Amazon author page for details.] Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing at Indiana University (winning many teaching awards), was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for 20+ years. This unique mix of learning, teaching, consulting, practice, and trading is reflected in every page. This revised 6th edition gives clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to trading. The presentation does not go far beyond basic Black-Scholes for three reasons: First, a novice need not go far beyond Black-Scholes to make money in the options markets; Second, all high-level option pricing theory is simply an extension of Black-Scholes; and Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here. The trading advice does not go far beyond elementary call and put positions because more complex trades are simply combinations of these. UNIQUE SELLING POINTS -The basic intuition you need to trade options for the first time, or interview for an options job. -Honest advice about trading: there is no simple way to beat the markets, but if you have skill this advice can help make you money, and if you have no skill but still choose to trade, this advice can reduce your losses. -Full immersion treatment of transactions costs (T-costs). -Lessons from trading stated in simple terms. -Stylized facts about the markets (e.g., how to profit from reversals, when are T-costs highest/lowest during the trading day, implications of the market for corporate control, etc.). -How to apply European-style Black-Scholes pricing to the trading of American-style options. -Leverage through margin trading compared to leverage through options, including worked spreadsheet examples. -Black-Scholes pricing code for HP17B, HP19B, and HP12C. -Five accompanying Excel sheets: forecast T-costs for options using simple models; explore option sensitivities including the Greeks; compare stock trading to option trading; GameStop example; and, explore P(ever ITM). -Practitioner Bloomberg Terminal screenshots to aid learning. -Simple discussion of continuously-compounded returns. -Introduction to "paratrading" (trading stocks side-by-side with options). -Unique "regrets" treatment of early exercise decisions and trade-offs for American-style calls and puts. -Unique discussion of put-call parity and option pricing. -How to calculate Black-Scholes in your head in 10 seconds (also in Heard on The Street: Quantitative Questions from Wall Street Job Interviews). -Special attention to arithmetic Brownian motion with general pricing formulae and comparisons of Bachelier (1900) with Black-Scholes. -Careful attention to the impact of dividends in analytical American option pricing. -Dimensional analysis and the adequation formula (relating FX call and FX put prices through transformed Black-Scholes formulae). -Intuitive review of risk-neutral pricing/probabilities and how and why these are related to physical pricing/probabilities. -Careful distinction between the early Merton (non-risk-neutral) hedging-type argument and later Cox-Ross/Harrison-Kreps risk-neutral pricing -Simple discussion of Monte-Carlo methods in science and option pricing. -Simple interpretations of the Black-Scholes formula and PDE and implications for trading. -Careful discussion of conditional probabilities as they relate to Black-Scholes. -Intuitive treatment of high-level topics e.g., bond-numeraire interpretation of Black-Scholes (where N(d2) is P(ITM)) versus the stock-numeraire interpretation (where N(d1) is P(ITM)). -Introduction and discussion of the risk-neutral probability that a European-style call or put option is ever in the money during its life.
Book Synopsis The Journal of Computational Finance by :
Download or read book The Journal of Computational Finance written by and published by . This book was released on 2004 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Financial Decision Making under Uncertainty by : Giorgio Consigli
Download or read book Optimal Financial Decision Making under Uncertainty written by Giorgio Consigli and published by Springer. This book was released on 2016-10-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of this volume is primarily to analyze from different methodological perspectives similar valuation and optimization problems arising in financial applications, aimed at facilitating a theoretical and computational integration between methods largely regarded as alternatives. Increasingly in recent years, financial management problems such as strategic asset allocation, asset-liability management, as well as asset pricing problems, have been presented in the literature adopting formulation and solution approaches rooted in stochastic programming, robust optimization, stochastic dynamic programming (including approximate SDP) methods, as well as policy rule optimization, heuristic approaches and others. The aim of the volume is to facilitate the comprehension of the modeling and methodological potentials of those methods, thus their common assumptions and peculiarities, relying on similar financial problems. The volume will address different valuation problems common in finance related to: asset pricing, optimal portfolio management, risk measurement, risk control and asset-liability management. The volume features chapters of theoretical and practical relevance clarifying recent advances in the associated applied field from different standpoints, relying on similar valuation problems and, as mentioned, facilitating a mutual and beneficial methodological and theoretical knowledge transfer. The distinctive aspects of the volume can be summarized as follows: Strong benchmarking philosophy, with contributors explicitly asked to underline current limits and desirable developments in their areas. Theoretical contributions, aimed at advancing the state-of-the-art in the given domain with a clear potential for applications The inclusion of an algorithmic-computational discussion of issues arising on similar valuation problems across different methods. Variety of applications: rarely is it possible within a single volume to consider and analyze different, and possibly competing, alternative optimization techniques applied to well-identified financial valuation problems. Clear definition of the current state-of-the-art in each methodological and applied area to facilitate future research directions.
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 2015-03-03 with total page 672 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.
Book Synopsis Basic Black-Scholes by : Timothy Falcon Crack
Download or read book Basic Black-Scholes written by Timothy Falcon Crack and published by . This book was released on 2021-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Note: eBook now available; see Amazon author page for details.] THE AUTHOR: Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing at Indiana University (winning many teaching awards), was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for over 20 years. This unique mix of learning, teaching, consulting, practice, and trading is reflected in every page. This revised 5th edition gives clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to trading. The presentation does not go far beyond basic Black-Scholes for three reasons: First, a novice need not go far beyond Black-Scholes to make money in the options markets; Second, all high-level option pricing theory is simply an extension of Black-Scholes; and Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here. The trading advice does not go far beyond elementary call and put positions because more complex trades are simply combinations of these. UNIQUE SELLING POINTS -The basic intuition you need to trade options for the first time, or interview for an options job. -Honest advice about trading: there is no simple way to beat the markets, but if you have skill this advice can help make you money, and if you have no skill but still choose to trade, this advice can reduce your losses. -Full immersion treatment of transactions costs (T-costs). -Lessons from trading stated in simple terms. -Stylized facts about the markets (e.g., how to profit from reversals, when are T-costs highest/lowest during the trading day, implications of the market for corporate control, etc.). -How to apply European-style Black-Scholes pricing to the trading of American-style options. -Leverage through margin trading compared to leverage through options, including worked spreadsheet example. -Black-Scholes pricing code for the HP17B, HP19B, and HP12C. -Three downloadable spreadsheets. One allows the user to forecast T-costs for option positions using simple models. Another allows the user to explore option sensitivities including the Greeks. -Practitioner Bloomberg Terminal screenshots to aid learning. -Simple discussion of continuously-compounded returns. -Introduction to "paratrading" (trading stocks side-by-side with options to generate additional profit). -Unique "regrets" treatment of early exercise decisions and trade-offs for American-style calls and puts. -Unique discussion of put-call parity and option pricing. -How to calculate Black-Scholes in your head in 10 seconds (also in Heard on The Street: Quantitative Questions from Wall Street Job Interviews). -Special attention to arithmetic Brownian motion with general pricing formulae and comparisons to Bachelier (1900) and Black-Scholes. -Careful attention to the impact of dividends in analytical American option pricing. -Dimensional analysis and the adequation formula (relating FX call and FX put prices through transformed Black-Scholes formulae). -Intuitive review of risk-neutral pricing/probabilities and how and why these are related to physical pricing/probabilities. -Careful distinction between the early Merton (non-risk-neutral) hedging-type argument and later Cox-Ross/Harrison-Kreps risk-neutral pricing -Simple discussion of Monte-Carlo methods in science and option pricing. -Simple interpretations of the Black-Scholes formula and PDE and implications for trading. -Careful discussion of conditional probabilities as they relate to Black-Scholes. -Intuitive treatment of high-level topics e.g., bond-numeraire interpretation of Black-Scholes (where N(d2) is P(ITM)) versus the stock-numeraire interpretation (where N(d1) is P(ITM)). -Introduction and discussion of the risk-neutral probability that a European-style call or put option is ever in the money during its life.
Book Synopsis Vinzenz Bronzin's Option Pricing Models by : Wolfgang Hafner
Download or read book Vinzenz Bronzin's Option Pricing Models written by Wolfgang Hafner and published by Springer Science & Business Media. This book was released on 2009-11-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1908, Vinzenz Bronzin, a professor of mathematics at the Accademia di Commercio e Nautica in Trieste, published a booklet in German entitled Theorie der Prämiengeschäfte (Theory of Premium Contracts) which is an old type of option contract. Almost like Bachelier’s now famous dissertation (1900), the work seems to have been forgotten shortly after it was published. However, almost every element of modern option pricing can be found in Bronzin’s book. He derives option prices for an illustrative set of distributions, including the Normal. - This volume includes a reprint of the original German text, a translation, as well as an appreciation of Bronzin's work from various perspectives (economics, history of finance, sociology, economic history) including some details about the professional life and circumstances of the author. The book brings Bronzin's early work to light again and adds an almost forgotten piece of research to the theory of option pricing.
Download or read book Options written by Stewart Hodges and published by Manchester University Press. This book was released on 1992 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Early Exercise of American Put Options by : Malin Engstrom
Download or read book Early Exercise of American Put Options written by Malin Engstrom and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate how well the actual exercise behaviour of American put options corresponds to the early exercise rules using Swedish equity option data. The numerical binomial model according to Cox et al. (1979) is used to compute a critical exercise price, above which a put option should be exercised early, in order to establish the theoretically optimal early exercise behaviour. We find several examples of irrational early exercise behaviour, both faulty actual exercises and failures to exercise. Most of the decisions to exercise the put options conform to rational exercise behaviour, whereas a large number of failures to exercise are found. This suggests that traders do not monitor their put option positions with sufficient care. By carrying out a sensitivity analysis, we conclude that the results persist after taking into account transaction costs associated with option exercise and the possibility that the volatility is not correctly estimated. A direct model-independent test of the failures to exercise, where the exercise value of the option is compared to its market bid price, shows that the results cannot be explained by the choice of model. Most of the found failures are regarded as failures also according to the direct test. Finally, we compute the average loss due to incorrect exercise behaviour in order to assess the economic significance of the results. Although occurring frequently, the failures to exercise do not appear to be costly.
Book Synopsis Trading and Pricing Financial Derivatives by : Patrick Boyle
Download or read book Trading and Pricing Financial Derivatives written by Patrick Boyle and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-12-17 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trading and Pricing Financial Derivatives is an introduction to the world of futures, options, and swaps. Investors who are interested in deepening their knowledge of derivatives of all kinds will find this book to be an invaluable resource. The book is also useful in a very applied course on derivative trading. The authors delve into the history of options pricing; simple strategies of options trading; binomial tree valuation; Black-Scholes option valuation; option sensitivities; risk management and interest rate swaps in this immensely informative yet easy to comprehend work. Using their vast working experience in the financial markets at international investment banks and hedge funds since the late 1990s and teaching derivatives and investment courses at the Master's level, Patrick Boyle and Jesse McDougall put forth their knowledge and expertise in clearly explained concepts. This book does not presuppose advanced mathematical knowledge, though it is presented for completeness for those that may benefit from it, and is designed for a general audience, suitable for beginners through to those with intermediate knowledge of the subject.
