by Daniel J. Duffy
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Product Description
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.
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Average Customer Review:
0 of 0 people found the following review helpful:
Not a book to learn PDEs, 2008-10-11
I agree with the above reviewer, that this book presents many facts from PDE theory without providing any motivation or explaining roots of the problem to be addressed. Many topics in this book treated only superficially and final result presented without proper explanation. Also, it seems there is no logical link between topics scattered in 33 short chapters of this book. The treatment of topics neither advanced not detailed. At the same time this book is unsuitable for the beginners, because it i hard to follow the author's thoughts and most of the results are simply presented without derivation and providing necessary preliminaries.
Conclusion: If you are new to PDE theory and want to learn application of PDEs to derivative modeling, read "Option Pricing: Mathematical Models and Computation" by Wilmott et al., volume 2 of Shreve's "Stochastic calculus for finance", or Wilmott's "Paul Wilmott on Quantitative Finance".
3 of 6 people found the following review helpful:
 totally useless!!!, 2008-03-21
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!
3 of 3 people found the following review helpful:
 A practical approach to finite difference methods, 2006-11-09
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.
2 of 3 people found the following review helpful:
Well Done, 2006-11-06
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.
2 of 3 people found the following review helpful:
Need more books like this one, 2006-07-05
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.
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