The Valuation Of American Barrier Options Using The Decomposition Technique
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| Author | : Bin Gao |
| Publisher | : |
| Total Pages | : |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call quot;symmetryquot; relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.
| Author | : Marti G. Subrahmanyam |
| Publisher | : |
| Total Pages | : 44 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
In this paper, we propose an alternative approach for pricing and hedging non-standard American options. In principle, the proposed approach applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of barrier options, an important example of path-dependent options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary - homogeneity in price parameters and time-invariance - for American options. In addition, some new put-call ``symmetryquot; relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of option prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is substantially faster than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.
| Author | : Espen Gaarder Haug |
| Publisher | : John Wiley & Sons |
| Total Pages | : 400 |
| Release | : 2013-10-18 |
| Genre | : Business & Economics |
| ISBN | : 1118836820 |
Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models
| Author | : Thomas S. Y. Ho |
| Publisher | : Oxford University Press |
| Total Pages | : 762 |
| Release | : 2004-01-15 |
| Genre | : Business & Economics |
| ISBN | : 0199923981 |
The essential premise of this book is that theory and practice are equally important in describing financial modeling. In it the authors try to strike a balance in their discussions between theories that provide foundations for financial models and the institutional details that provide the context for applications of the models. The book presents the financial models of stock and bond options, exotic options, investment grade and high-yield bonds, convertible bonds, mortgage-backed securities, liabilities of financial institutions--the business model and the corporate model. It also describes the applications of the models to corporate finance. Furthermore, it relates the models to financial statements, risk management for an enterprise, and asset/liability management with illiquid instruments. The financial models are progressively presented from option pricing in the securities markets to firm valuation in corporate finance, following a format to emphasize the three aspects of a model: the set of assumptions, the model specification, and the model applications. Generally, financial modeling books segment the world of finance as "investments," "financial institutions," "corporate finance," and "securities analysis," and in so doing they rarely emphasize the relationships between the subjects. This unique book successfully ties the thought processes and applications of the financial models together and describes them as one process that provides business solutions. Created as a companion website to the book readers can visit www.thomasho.com to gain deeper understanding of the book's financial models. Interested readers can build and test the models described in the book using Excel, and they can submit their models to the site. Readers can also use the site's forum to discuss the models and can browse server based models to gain insights into the applications of the models. For those using the book in meetings or class settings the site provides Power Point descriptions of the chapters. Students can use available question banks on the chapters for studying.
| Author | : Mkhululi Dlamini |
| Publisher | : |
| Total Pages | : 100 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
| Author | : V.V. Rykov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 465 |
| Release | : 2010-11-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0817649719 |
The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.
| Author | : Elyès Jouini |
| Publisher | : Cambridge University Press |
| Total Pages | : 324 |
| Release | : 2001 |
| Genre | : Derivative securities |
| ISBN | : 9780521792370 |
This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.
| Author | : Marco Avellaneda |
| Publisher | : World Scientific |
| Total Pages | : 363 |
| Release | : 2002-01-18 |
| Genre | : Mathematics |
| ISBN | : 9814490598 |
This invaluable book contains lectures presented at the Courant Institute's Mathematical Finance Seminar. The audience consisted of academics from New York University and other universities, as well as practitioners from investment banks, hedge funds and asset-management firms.
| Author | : Yue-Kuen Kwok |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 541 |
| Release | : 2008-07-10 |
| Genre | : Mathematics |
| ISBN | : 3540686886 |
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.
| Author | : Sebastian Paik |
| Publisher | : University of Bamberg Press |
| Total Pages | : 365 |
| Release | : 2014 |
| Genre | : |
| ISBN | : 3863091787 |
