Finite Difference Methods in Financial Engineering

A Partial Differential Equation Approach

Daniel J. Duffy

430 pages, parution le 24/02/2006

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Résumé

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.

L'auteur - Daniel J. Duffy

Daniel J. Duffy has been involved in software development projects using C++ and object-oriented design techniques since 1988. He organized the first C++ course in the Netherlands in 1989 and has worked on a variety of C++ projects in areas such as computer graphics, optical technology, process control and quantitative finance systems. In 1993 he worked on an early version of a large object-oriented system for derivatives' pricing and hedging models. He is designer/trainer and has trained mote than 2000 C++ developers in recent years.

A companion book to the current one is "Financial instrument pricing using C++" (Wiley 2004). Since 1996 he has written seven books on object-oriented design and programming. Daniel Duffy has a Phd in Numerical Analysis from Trinity College Dublin. He lives in the Netherlands with his wife Ilona and son Brendan.

Sommaire

The continuous theory of partial differential equations
Finite difference methods: the fundamentals
Applying fdm to one-factor instrument pricing
FDM for multidimensional problems
Applying FDM to multi-factor instrument pricing
Free and moving boundary value problems
Design and implementation in Cc++

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Daniel J. Duffy
Parution	24/02/2006
Nb. de pages	430
Format	17,5 x 25,5
Couverture	Relié
Poids	1015g
Intérieur	Noir et Blanc
EAN13	9780470858820
ISBN13	978-0-470-85882-0