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Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach - Hardcover

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Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

Daniel Duffy is a numerical analyst who has been working in the IT business since 1979. He has been involved in the analysis, design and implementation of systems using object-oriented, component and (more recently) intelligent agent technologies to large industrial and financial applications. As early as 1993 he was involved in C++ projects for risk management and options applications with a large Dutch bank. His main interest is in finding robust and scalable numerical schemes that approximate the partial differential equations that model financial derivatives products. He has an M.Sc. in the Finite Element Method first-order hyperbolic systems and a Ph.D. in robust finite difference methods for convection-diffusion partial differential equations. Both degrees are from Trinity College, Dublin, Ireland.
Daniel Duffy is founder of Datasim Education and Datasim Component Technology, two companies involved in training, consultancy and software development.

"About this title" may belong to another edition of this title.

  • PublisherWiley
  • Publication date2006
  • ISBN 10 0470858826
  • ISBN 13 9780470858820
  • BindingHardcover
  • LanguageEnglish
  • Number of pages448
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Hardcover. Condition: Fine. Dust Jacket Condition: Fine. Book: Fine/+, 2006 (illustrator). 1st Edition. Book: Fine/+, $175.77 0470858826 FINITE DIFFERENCE METHODS in FINANCIAL ENGINEERING: a PARTIAL DIFFERENTIAL EQUATION APPROACH, Including C/D and Dust Jacket. * DUFFY, Daniel J. John Wiley & Sons England * * * * * 2006 1sT Edition, 1sT Printing H/c. Top Green And Bottom Black Pieces, Center Is Golden Colored Spine With Title In 0ff~White Black And Grey Letters, Dust Jacket: Fine/As New/, Slightest Shelf, Edge And Corner Wear. Hard Book: Fine/+, 423 Numbered Pages, Printed On 0ff~White Paper, That Appear To Be Lightly Viewed And Are Clean And Tight To The Spine, In Fine/As New/ Condition. C/D UnOpened In Publisher`s Original Packet Inside Rear Cover. Dust Jacket: None. = No Odors, No Writing, No Names, No Rippling, Not Stuck Together, No Book Plate, Not X~Library, No Remainder Or Other Marks. This Item Will Be Sent In A = Mailing B0X = To Prevent Shipping Damage So That It Will Arrive In The Description Described. Description Applies To This B00K, Only. = This B00K Is Hard To Find, Will Be Packaged And Shipped Carefully, = To Avoid Shipping Damage And Will Make It, An Excellent Addition To Your Own Personal Library Collection, Or As A Gift, For The Discriminating Reader / Collector. = WORLD WIDE SHIPPING, AVAILABLE *. Seller Inventory # 016394

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Hardcover. Condition: new. Hardcover. 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 optionsEarly exercise features and approximation using front-fixing, penalty and variational methodsModelling stochastic volatility models using Splitting methodsCritique of ADI and Crank-Nicolson schemes; when they work and when 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 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. This is today's most complete and practical guide to finite difference methods and its applications to derivatives. The application of finite difference methods (FDM), long popular in areas such as fluid mechanics and heat transfer, has become increasingly vital for pricing derivative products in today's global markets. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780470858820

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