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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.
From the Back Cover
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.
The goal of this book is to develop robust, accurate and efficient numerical methods to price a number of derivative products in quantitative finance. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Customer Reviews
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!
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
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