Finite Difference Methods In Financial Engineering

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Finite Difference Methods in Financial Engineering

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 51,8 Mb
Release : 2013-10-28
Category : Business & Economics
ISBN : 9781118856482

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Finite Difference Methods in Financial Engineering by Daniel J. Duffy Pdf

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.

Derivative Securities and Difference Methods

Author : You-lan Zhu,Xiaonan Wu,I-Liang Chern,Zhi-zhong Sun
Publisher : Springer Science & Business Media
Page : 663 pages
File Size : 46,8 Mb
Release : 2013-07-04
Category : Mathematics
ISBN : 9781461473060

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Derivative Securities and Difference Methods by You-lan Zhu,Xiaonan Wu,I-Liang Chern,Zhi-zhong Sun Pdf

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

Numerical Methods in Computational Finance

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 551 pages
File Size : 53,8 Mb
Release : 2022-03-14
Category : Business & Economics
ISBN : 9781119719724

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Numerical Methods in Computational Finance by Daniel J. Duffy Pdf

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

Pricing Financial Instruments

Author : Domingo Tavella,Curt Randall
Publisher : Wiley
Page : 256 pages
File Size : 45,8 Mb
Release : 2000-04-21
Category : Business & Economics
ISBN : 0471197602

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Pricing Financial Instruments by Domingo Tavella,Curt Randall Pdf

Numerical methods for the solution of financial instrument pricingequations are fast becoming essential for practitioners of modernquantitative finance. Among the most promising of these newcomputational finance techniques is the finite differencemethod-yet, to date, no single resource has presented a quality,comprehensive overview of this revolutionary quantitative approachto risk management. Pricing Financial Instruments, researched and written by DomingoTavella and Curt Randall, two of the chief proponents of the finitedifference method, presents a logical framework for applying themethod of finite difference to the pricing of financialderivatives. Detailing the algorithmic and numerical proceduresthat are the foundation of both modern mathematical finance and thecreation of financial products-while purposely keeping mathematicalcomplexity to a minimum-this long-awaited book demonstrates how thetechniques described can be used to accurately price simple andcomplex derivative structures. From a summary of stochastic pricing processes and arbitragepricing arguments, through the analysis of numerical schemes andthe implications of discretization-and ending with case studiesthat are simple yet detailed enough to demonstrate the capabilitiesof the methodology- Pricing Financial Instruments explores areasthat include: * Pricing equations and the relationship be-tween European andAmerican derivatives * Detailed analyses of different stability analysisapproaches * Continuous and discrete sampling models for path dependentoptions * One-dimensional and multi-dimensional coordinatetransformations * Numerical examples of barrier options, Asian options, forwardswaps, and more With an emphasis on how numerical solutions work and how theapproximations involved affect the accuracy of the solutions,Pricing Financial Instruments takes us through doors opened wide byBlack, Scholes, and Merton-and the arbitrage pricing principlesthey introduced in the early 1970s-to provide a step-by-stepoutline for sensibly interpreting the output of standard numericalschemes. It covers the understanding and application of today'sfinite difference method, and takes the reader to the next level ofpricing financial instruments and managing financial risk. Praise for Pricing Financial Instruments "Pricing Financial Instruments is the first broad and accessibletreatment of finite difference methods for pricing derivativesecurities. The authors have taken great care to clearly explainboth the origins of the pricing problems in a financial setting, aswell as many practical aspects of their numerical methods. The bookcovers a wide variety of applications, such as American options andcredit derivatives. Both financial analysts and academicasset-pricing specialists will want to own a copy."-Darrell Duffie,Professor of Finance Stanford University "In my experience, finite difference methods have proven to be asimple yet powerful tool for numerically solving the evolutionaryPDEs that arise in modern mathematical finance. This book shouldfinally dispel the widely held notion that these methods aresomehow difficult or abstract. I highly recommend it to anyoneinterested in the implementation of these methods in the financialarena."-Peter Carr, Principal Bank of America Securities "A very comprehensive treatment of the application of finitedifference techniques to derivatives finance. Practitioners willfind the many extensive examples very valuable and students willappreciate the rigorous attention paid to the many subtleties offinite difference techniques."-Francis Longstaff, Professor TheAnderson School at UCLA "The finite difference approach is central to the numerical pricingof financial securities. This book gives a clear and succinctintroduction to this important subject. Highly recommended."-MarkBroadie, Associate Professor School of Business, ColumbiaUniversity For updates on new and bestselling Wiley Finance books:wiley.com/wbns

Finite Difference Methods for Ordinary and Partial Differential Equations

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 53,9 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Financial Engineering

Author : Keith Cuthbertson,Dirk Nitzsche
Publisher : John Wiley & Sons
Page : 802 pages
File Size : 44,7 Mb
Release : 2001-06-08
Category : Business & Economics
ISBN : 9780471495840

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Financial Engineering by Keith Cuthbertson,Dirk Nitzsche Pdf

This text provides a thorough treatment of futures, 'plain vanilla' options and swaps as well as the use of exotic derivatives and interest rate options for speculation and hedging. Pricing of options using numerical methods such as lattices (BOPM), Mone Carlo simulation and finite difference methods, in additon to solutions using continuous time mathematics, are also covered. Real options theory and its use in investment appraisal and in valuing internet and biotechnology companies provide cutting edge practical applications. Practical risk management issues are examined in depth. Alternative models for calculating Value at Risk (market risk) and credit risk provide the throretical basis for a practical and timely overview of these areas of regulatory policy. This book is designed for courses in derivatives and risk management taken by specialist MBA, MSc Finance students or final year undergraduates, either as a stand-alone text or as a follow-on to Investments: Spot and Derivatives Markets by the same authors. The authors adopt a real-world emphasis throughout, and include features such as: * topic boxes, worked examples and learning objectives * Financial Times and Wall Street Journal newspaper extracts and analysis of real world cases * supporting web site including Lecturer's Resource Pack and Student Centre with interactive Excel and GAUSS software

Derivatives

Author : Paul Wilmott
Publisher : Unknown
Page : 778 pages
File Size : 41,9 Mb
Release : 1998-12-08
Category : Business & Economics
ISBN : UOM:39015058966063

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Derivatives by Paul Wilmott Pdf

Accompanying computer optical disc contains 'demos of commercial software, spreadsheets and code illustrating models and methods from the book, cutting-edge research articles..., data document and demo from CrashMetrics, the Value at Risk methodology'. (book)

Computational Methods in Finance

Author : Ali Hirsa
Publisher : CRC Press
Page : 440 pages
File Size : 53,9 Mb
Release : 2016-04-19
Category : Business & Economics
ISBN : 9781466576049

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Computational Methods in Finance by Ali Hirsa Pdf

As today's financial products have become more complex, quantitative analysts, financial engineers, and others in the financial industry now require robust techniques for numerical analysis. Covering advanced quantitative techniques, Computational Methods in Finance explains how to solve complex functional equations through numerical methods. The f

Numerical Methods in Finance and Economics

Author : Paolo Brandimarte
Publisher : John Wiley & Sons
Page : 501 pages
File Size : 46,8 Mb
Release : 2013-06-06
Category : Mathematics
ISBN : 9781118625576

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Numerical Methods in Finance and Economics by Paolo Brandimarte Pdf

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.

Numerical Partial Differential Equations in Finance Explained

Author : Karel in 't Hout
Publisher : Springer
Page : 128 pages
File Size : 49,5 Mb
Release : 2017-09-02
Category : Business & Economics
ISBN : 9781137435699

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Numerical Partial Differential Equations in Finance Explained by Karel in 't Hout Pdf

This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.

Finite Difference Computing with PDEs

Author : Hans Petter Langtangen,Svein Linge
Publisher : Springer
Page : 522 pages
File Size : 53,5 Mb
Release : 2017-06-21
Category : Computers
ISBN : 9783319554563

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Finite Difference Computing with PDEs by Hans Petter Langtangen,Svein Linge Pdf

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Numerical Methods in Finance

Author : Paolo Brandimarte
Publisher : John Wiley & Sons
Page : 429 pages
File Size : 46,7 Mb
Release : 2003-10-13
Category : Mathematics
ISBN : 9780471461692

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Numerical Methods in Finance by Paolo Brandimarte Pdf

Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.

Financial Engineering with Finite Elements

Author : Juergen Topper
Publisher : John Wiley & Sons
Page : 378 pages
File Size : 48,6 Mb
Release : 2005-06-24
Category : Business & Economics
ISBN : 9780470012918

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Financial Engineering with Finite Elements by Juergen Topper Pdf

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

Introduction to C++ for Financial Engineers

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 405 pages
File Size : 53,9 Mb
Release : 2013-10-24
Category : Business & Economics
ISBN : 9781118856468

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Introduction to C++ for Financial Engineers by Daniel J. Duffy Pdf

This book introduces the reader to the C++ programming language and how to use it to write applications in quantitative finance (QF) and related areas. No previous knowledge of C or C++ is required -- experience with VBA, Matlab or other programming language is sufficient. The book adopts an incremental approach; starting from basic principles then moving on to advanced complex techniques and then to real-life applications in financial engineering. There are five major parts in the book: C++ fundamentals and object-oriented thinking in QF Advanced object-oriented features such as inheritance and polymorphism Template programming and the Standard Template Library (STL) An introduction to GOF design patterns and their applications in QF Applications The kinds of applications include binomial and trinomial methods, Monte Carlo simulation, advanced trees, partial differential equations and finite difference methods. This book includes a companion website with all source code and many useful C++ classes that you can use in your own applications. Examples, test cases and applications are directly relevant to QF. This book is the perfect companion to Daniel J. Duffy’s book Financial Instrument Pricing using C++ (Wiley 2004, 0470855096 / 9780470021620)

Handbooks in Operations Research and Management Science: Financial Engineering

Author : John R. Birge,Vadim Linetsky
Publisher : Elsevier
Page : 1026 pages
File Size : 48,6 Mb
Release : 2007-11-16
Category : Business & Economics
ISBN : 0080553257

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Handbooks in Operations Research and Management Science: Financial Engineering by John R. Birge,Vadim Linetsky Pdf

The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.