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Implementation Of Finite Difference Technique For Exotic Double Barrier Options
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Book Synopsis Finite Difference Methods in Financial Engineering by : Daniel J. Duffy
Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Book Synopsis Operator Theory and Harmonic Analysis by : Alexey N. Karapetyants
Download or read book Operator Theory and Harmonic Analysis written by Alexey N. Karapetyants and published by Springer Nature. This book was released on 2021-08-31 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and applications of probability and statistics in the context of general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multi-parameter objects required when considering operators and objects with variable parameters.
Book Synopsis How to Implement Market Models Using VBA by : Francois Goossens
Download or read book How to Implement Market Models Using VBA written by Francois Goossens and published by John Wiley & Sons. This book was released on 2015-01-23 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible VBA coding for complex financial modelling How to Implement Market Models Using VBA makes solving complex valuation issues accessible to any financial professional with a taste for mathematics. With a focus on the clarity of code, this practical introductory guide includes chapters on VBA fundamentals and essential mathematical techniques, helping readers master the numerical methods to build an algorithm that can be used in a wide range of pricing problems. Coverage includes general algorithms, vanilla instruments, multi-asset instruments, yield curve models, interest rate exotics, and more, guiding readers thoroughly through pricing in the capital markets area. The companion website (http://implementmodinvba.com/) features additional VBA code and algorithmic techniques, and the interactive blog provides a forum for discussion of code with programmers and financial engineers, giving readers insight into the different applications and customisations possible for even more advanced problem solving.. Financial engineers implement models from a mathematical representation of an asset's performance by building a program that performs a valuation of securities based on this asset. How to Implement Market Models Using VBA makes this technical process understandable, with well-explained algorithms, VBA code, and accessible theoretical explanations. Decide which numerical method to use in which scenario Identify the necessary building blocks of an algorithm Write clear, functional VBA code for a variety of problems Apply algorithms to different instruments and models Designed for finance professionals, this book brings more accurate modelling within reach for anyone with interest in the market. For clearer code, patient explanation, and practical instruction, How to Implement Market Models Using VBA is an essential introductory guide.
Book Synopsis Implementing Models in Quantitative Finance: Methods and Cases by : Gianluca Fusai
Download or read book Implementing Models in Quantitative Finance: Methods and Cases written by Gianluca Fusai and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
Book Synopsis Exotic Options: A Guide To Second Generation Options (2nd Edition) by : Peter Guangping Zhang
Download or read book Exotic Options: A Guide To Second Generation Options (2nd Edition) written by Peter Guangping Zhang and published by World Scientific. This book was released on 1998-06-17 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first systematic and extensive book on exotic options. The book covers essentially all popular exotic options currently trading in the Over-the-Counter (OTC) market, from digitals, quantos, spread options, lookback options, Asian options, vanilla barrier options, to various types of exotic barrier options and other options. Each type of exotic options is largely written in a separate chapter, beginning with the basic concepts of the products and then moving on to how to price them in closed-form solutions. Many pricing formulae and analyses which have not previously appeared in the literature are included and illustrated with detailed examples. It will be of great interest to traders, marketers, analysts, risk managers, professors, graduate students, and anyone who is interested in what is going on in the rapidly changing financial market.
Book Synopsis Advances in Finance and Stochastics by : Klaus Sandmann
Download or read book Advances in Finance and Stochastics written by Klaus Sandmann and published by Springer Science & Business Media. This book was released on 2002-04-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.
Book Synopsis Derivative Securities and Difference Methods by : You-lan Zhu
Download or read book Derivative Securities and Difference Methods written by You-lan Zhu and published by Springer Science & Business Media. This book was released on 2013-07-04 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts. In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added. Review of first edition: “...the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS
Book Synopsis The Best of Wilmott 2 by : Paul Wilmott
Download or read book The Best of Wilmott 2 written by Paul Wilmott and published by John Wiley & Sons. This book was released on 2006-02-22 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Team at Wilmott is very proud to present this compilation of Wilmott magazine articles and presentations from our second year. We have selected some of the very best in cutting-edge research, and the most illuminating of our regular columns. The technical papers include state-of-the-art pricing tools and models. You'll notice there's a bias towards volatility modelling in the book. Of course, it's one of my favourite topics, but volatility is also the big unknown as far as pricing and hedging is concerned. We present research in this area from some of the best newcomers in this field. You'll see ideas that make a mockery of 'received wisdom,' ideas that are truly paradigm shattering - for we aren't content with a mere 'shift.' We know you'll enjoy it! The Best of Wilmott will return again next year...
Book Synopsis Financial Derivatives by : Rob Quail
Download or read book Financial Derivatives written by Rob Quail and published by John Wiley & Sons. This book was released on 2009-10-15 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential insights on the various aspects of financial derivatives If you want to understand derivatives without getting bogged down by the mathematics surrounding their pricing and valuation, Financial Derivatives is the book for you. Through in-depth insights gleaned from years of financial experience, Robert Kolb and James Overdahl clearly explain what derivatives are and how you can prudently use them within the context of your underlying business activities. Financial Derivatives introduces you to the wide range of markets for financial derivatives. This invaluable guide offers a broad overview of the different types of derivatives-futures, options, swaps, and structured products-while focusing on the principles that determine market prices. This comprehensive resource also provides a thorough introduction to financial derivatives and their importance to risk management in a corporate setting. Filled with helpful tables and charts, Financial Derivatives offers a wealth of knowledge on futures, options, swaps, financial engineering, and structured products. Discusses what derivatives are and how you can prudently implement them within the context of your underlying business activities Provides thorough coverage of financial derivatives and their role in risk management Explores financial derivatives without getting bogged down by the mathematics surrounding their pricing and valuation This informative guide will help you unlock the incredible potential of financial derivatives.
Book Synopsis Numerical Methods in Finance and Economics by : Paolo Brandimarte
Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
Book Synopsis Meshfree Approximation Methods with MATLAB by : Gregory E. Fasshauer
Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
Book Synopsis Derivative Securities and Difference Methods by : You-lan Zhu
Download or read book Derivative Securities and Difference Methods written by You-lan Zhu and published by Springer Science & Business Media. This book was released on 2004-08-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies pricing financial derivatives with a partial differential equation approach. The treatment is mathematically rigorous and covers a variety of topics in finance including forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, lookback options, interest rate models, interest rate derivatives, swaps, caps, floors, and collars. Each chapter concludes with exercises.
Book Synopsis journal of financial econonomics by :
Download or read book journal of financial econonomics written by and published by . This book was released on 2003 with total page 1098 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Financial Engineering with Finite Elements by : Juergen Topper
Download or read book Financial Engineering with Finite Elements written by Juergen Topper and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing of derivative instruments has always been a highly complex and time-consuming activity. Advances in technology, however, have enabled much quicker and more accurate pricing through mathematical rather than analytical models. In this book, the author bridges the divide between finance and mathematics by applying this proven mathematical technique to the financial markets. Utilising practical examples, the author systematically describes the processes involved in a manner accessible to those without a deep understanding of mathematics. * Explains little understood techniques that will assist in the accurate more speedy pricing of options * Centres on the practical application of these useful techniques * Offers a detailed and comprehensive account of the methods involved and is the first to explore the application of these particular techniques to the financial markets
Book Synopsis Implementing Derivatives Models by : Les Clewlow
Download or read book Implementing Derivatives Models written by Les Clewlow and published by . This book was released on 1998 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tools for Computational Finance by : Rüdiger U. Seydel
Download or read book Tools for Computational Finance written by Rüdiger U. Seydel and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tools for Computational Finance offers a clear explanation of computational issues arising in financial mathematics. The new third edition is thoroughly revised and significantly extended, including an extensive new section on analytic methods, focused mainly on interpolation approach and quadratic approximation. Other new material is devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation. New figures, more exercises, and expanded background material make this guide a real must-to-have for everyone working in the world of financial engineering.
Book Synopsis Uncertain Volatility Models by : Robert Buff
Download or read book Uncertain Volatility Models written by Robert Buff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
