cdc-coteauxdegaronne
» » Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach
eBook Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach ePub

eBook Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach ePub

by Daniel J. Duffy

  • ISBN: 0470858826
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Daniel J. Duffy
  • Language: English
  • Publisher: Wiley (May 12, 2006)
  • Pages: 442
  • ePub book: 1528 kb
  • Fb2 book: 1493 kb
  • Other: rtf azw mbr lrf
  • Rating: 4.9
  • Votes: 496

Description

In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives . Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM).

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)

A splitting implicit-explicit (SIMEX) scheme for solving a partial Fokker-Planck equation related to a jump-diffusion process is investigated.

A splitting implicit-explicit (SIMEX) scheme for solving a partial Fokker-Planck equation related to a jump-diffusion process is investigated.

Daniel . uffy introduces Finite Difference methods for solving partial differential equations that arise in numerical pricing of derivatives. Having bought many books in Financial Engineering this is one of the most useful. There are seven sections in the book. They are: Part I The Continuous Theory of Partial Differential Equations - A short introduction to partial differential equations and their applications to financial engineering. The source code is atleast alot better than the other books that claim to be the best.

In this book we employ partial differential equations (PDE) to describe a. . Daniel Duffy is a numerical analyst who has been working in the IT business since 1979.

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. 32 MB·703 Downloads·New! Numerical Methods for Partial Differential Equations: Finite Difference and. Handbook on the Physics and Chemistry of Rare Earths. 33 MB·11,318 Downloads·New!. An Introduction to Differential Equations: With Difference Equations, Fourier Series, and Partial. 64 MB·1,817 Downloads·New!

Finite difference methods in nancial engineering : a partial differential equation approach, Daniel J. Duffy. 2 An Introduction to Partial Differential Equations . Introduction and objectives . Partial differential equations . Specialisations . 1 Elliptic equations .

Finite difference methods in nancial engineering : a partial differential equation approach, Daniel J. p. cm. ISBN-13: 978-0-470-85882-0. ISBN-10: 0-470-85882-6. 2. Derivative thematical models. 3. Finite differences. 2 Free boundary value problems . Parabolic partial differential equations . 1 Special cases . Hyperbolic equations .

oceedings{Duffy2006FiniteDM, title {Finite Difference Methods in Financial Engineering: A Partial . Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing.

oceedings{Duffy2006FiniteDM, title {Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach}, author {Daniel J. Duffy}, year {2006} }. Daniel J.

Описание: 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.

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

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.

Find many great new & used options and get the best deals for Finite Difference Methods in Financial Engineering: A Partial . Additional Product Features. Place of Publication.

Additional Product Features.

The world of quantitative finance (QF) is one of the fastestgrowing areas of research and its practical applications toderivatives pricing problem. Since the discovery of the famousBlack-Scholes equation in the 1970's we have seen a surge in thenumber of models for a wide range of products such as plain andexotic options, interest rate derivatives, real options and manyothers. Gone are the days when it was possible to price thesederivatives analytically. For most problems we must resort to somekind of approximate method.

In this book we employ partial differential equations (PDE) todescribe a range of one-factor and multi-factor derivativesproducts such as plain European and American options, multi-assetoptions, Asian options, interest rate options and real options. PDEtechniques allow us to create a framework for modeling complex andinteresting derivatives products. Having defined the PDE problem wethen approximate it using the Finite Difference Method (FDM). Thismethod has been used for many application areas such as fluiddynamics, heat transfer, semiconductor simulation and astrophysics,to name just a few. In this book we apply the same techniques topricing real-life derivative products. We use both traditional (orwell-known) methods as well as a number of advanced schemes thatare making their way into the QF literature:

Crank-Nicolson, exponentially fitted and higher-order schemesfor one-factor and multi-factor optionsEarly exercise features and approximation using front-fixing,penalty and variational methodsModelling stochastic volatility models using SplittingmethodsCritique of ADI and Crank-Nicolson schemes; when they work andwhen they don't workModelling 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 toset up FDM algorithms, how to map these algorithms to C++ as wellas several working programs for one-factor and two-factor models.We also provide source code so that you can customize theapplications to suit your own needs.

Comments

Уou ll never walk alone Уou ll never walk alone
This book proved to be a useful reference for practical implementation of finite-difference methods for PDEs: several one- and multi-factor financial derivatives pricing models, including local volatility models and models with stochastic volatilities. The methods described in the text are stable, accurate and reasonably efficient. Stability of FD methods is obviously of top concern to the author (as it should be to readers as well), and he goes into extensive detail evaluating the stability of various techniques. The writing is clear and consistent, though a "notational" index or glossary would have been helpful, particularly in the early going. The author provides several practical examples, which lends a refreshing degree of concreteness to the book.
Maridor Maridor
Daniel J.Duffy introduces Finite Difference methods for solving partial differential equations that arise in numerical pricing of derivatives. There are seven sections in the book. They are:

Part I The Continuous Theory of Partial Differential Equations - A short introduction to partial differential equations and their applications to financial engineering.

Part II Finite Difference Methods: the Fundamentals - There are three chapters that introduce Finite Difference methods to approximate initial value and initial boundary value problems. Another two chapters apply the methods to Black-Scholes equation. He did a nice job to approximate the solutions to problems with small volatility or large drift,...

Part III Applying FDM to One-Factor Instrument Pricing

Part IV FDM for Multidimensional problems

Part V Applying FDM to Multi-Factor Instrument Pricing and

Part VI Free and Moving Boundary Value Problems

There are altogether 18 chapters (about 180 pages) that thoroughly introduce the application of FDM techniques to a wide range of options (pricing) modelling. The exposition is clear and concise.

The last part

Part VII Design and implementation In C++ - The last four chapters design for readers having programming literacy.

To fully appreciate the materials of the book, readers should have at least one year training in partial differential equations and knowledge in financial derivatives at about the same level as John Hull's book - Options, Futures and Other Derivatives, 5e.

If the book contains a few applications to real world data, it will be perfect to primers in this field.
Jube Jube
We have this book in our library and I wanted to use it for a financial engineering course.
I have gained sufficient traction in solving PDEs using the Explicit FDM approach - learnt from Paul Wilmott's Quantitative Finance.
Armed with that knowledge, I opened the book and sat to read and see if I could enhance my skills further. Unfortunately after upteen attempts, I am lost because I am unable to find a natural progression through the chapters. The book may appeal to someone with in depth knowledge in Quant Maths but definitely NOT for beginners/intermediate level readers.
The jumps in and between chapters is too much to handle at times so either you are a 100% Quant Math person - in that case perhaps you will be able to connect the dots or you are at my stage - you will fail to connect the dots miserably.
Walianirv Walianirv
I used this book to solve a rather difficult PDE and in the end i decided that a binomial tree approximation would save me time instead of reading this.
First it is not a beginer's book, second it wastes millions of precious time to the classification of PDEs in a very dense writting style cut in small chapters. In some cases it presents no proofs, or it assumes knowledge of mathematics that does not even cover. For example at some point syas that to check sth toy need Fourier and no presentation of the method is shown. In short to difficult to read, not for a beginner
Mejora Mejora
What a joke! This book claims to be adequate for those who have little or no knowledge in the field of PDEs and finite differnces (which is not my case), and believe me you will be just as ignorant after having read the book!

The book is divided into seven parts with the first one dealing with the general theory of PDEs, except that the information content is null! Even the heat equation is not fully solved, whether it is by separation of variables, where the solution is thrown at you in different cases, or by Fourier transform where the author takes the transform of the PDE then conveniently tells you that this can then be solved and converted back into the solution to the problem by "well known" techniques!! Prepostorous!! Furthermore, the entire book is simply a bunch well packed results and definitions with little or no insight as to their practical applications. You will simply learn the EXISTENCE of a certain number of techniques, however you will not have enough information to implement these or gain any insight into them! If you want to learn about PDEs, finite diffenences and their financial applications go for Wilmott, at least the latter won't waste your time!
Sarin Sarin
Having bought many books in Financial Engineering this is one of the most useful. The source code is atleast alot better than the other books that claim to be the best. I give this book 4 stars and recommend quants to buy this book.