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Chapter 5 deals with basic finite difference schemes for partial differential equations. In this simplified framework we may understand the difference between explicit and implicit methods, as well as the issues related to convergence and numerical stability. With respect to the first edition, I have added an outline of the Alternating Direction Implicit method to solve the two-dimensional heat equation, which is useful background for pricing multidimensional options.

This chapter can be safely skipped by students interested in the option pricing applications described in chapters 7, 8, and 9. However, it may be useful to students in Economics. It is also necessary background for the relatively advanced optimization models and methods which are covered in chapters 10, 11, and Chapter 7 is a new chapter which is devoted to binomial and trinomial lattices, which were not treated extensively in the first edition.

The main issues here are proper implementation and memory management. We also deal briefly with the estimation of option sensitivities the Greeks by Monte Carlo methods. Emphasis is on European-style options; pricing American options by Monte Carlo methods is a more advanced topic which must be analyzed within an appropriate framework, which is done in chapter The main reason for including this chapter is pricing American options by Monte Carlo simulation, which was not covered in the first edition but is gaining more and more importance.

I have decided to deal with this topic within an appropriate framework, which is dynamic stochastic optimization. In this chapter we just cover the essentials, which means discretetime and finite-horizon dynamic programs.

Nevertheless, we try to offer a reasonably firm understanding of these topics, both because of their importance in Economics and because understanding dynamic programming is helpful in understanding stochastic programming with recourse, which is the subject of the next chapter.

This is becoming a standard topic for people in Operations Research, whereas people in Economics are much more familiar with dynamic programming.

There are good reasons for this state of the matter, but from a methodological point of view I believe that it is very xx PREFACE important to compare this approach with dynamic programming; from a practical point of view, stochastic programming has an interesting potential both for dynamic portfolio management and for option hedging in incomplete markets.

Chapter 12 also deals with the relatively exotic topic of non-convex optimization. The main aim here is introducing mixed-integer programming, which can be used for portfolio management when practically relevant constraints call for the introduction of logical decision variables. We also deal, very shortly, with global optimization, i.

We also outline heuristic principles such as local search and genetic algorithms. They are useful to integrate simulation and optimization and are often used in computational economics. The appendix on probability and statistics is just a refresher which is offered for the sake of convenience.

The third appendix on AMPL is new, and it reflects the increased role of algebraic languages to describe complex optimization models.

AMPL is a modeling system offering access to a wide array of optimization solvers. The choice of AMPL is just based on personal taste and the fact that a demo version is available on the web. In fact, GAMS is probably much more common for economic applications, but the concepts are actually the same. This appendix is only required for chapters 11 and Finally, there are many more pages in this second edition: more than pages, whereas the first edition had about Actually, I had a choice: either including many more topics, such as interest-rate derivatives, or offering a more extended and improved coverage of what was already included in the first edition.

While there is indeed some new material, I preferred the second option.

Actually, the original plan of the book included two more chapters on interest-rate derivatives, as many readers complained about this lack in the first edition. While writing this increasingly long second edition, I switched to plan B, and interest-rate derivatives are just outlined in the second chapter to point out their peculiarities with respect to stock options.

In fact, when planning this new edition, many reviewers warned that there was little hope to cover interest-rate derivatives thoroughly in a limited amount of pages. They require a deeper understanding of risk-neutral pricing, interest rate modeling, and market practice.

I do believe that the many readers interested in this PREFACE xxi topic can use this book to build a solid basis in numerical methods, which is helpful to tackle the more advanced texts on interest-rate derivatives.

Interest-rate derivatives are not the only significant omission. I could also mention implied lattices and financial econometrics.

But since there are excellent books covering those topics and I see this one just as an entry point or a complement, I felt that it was more important to give a concrete understanding of the basics, including some less familiar topics.

Furthermore, the heavy burden it places on the reader tends to overshadow the underlying concepts, which are the real subject of the book.

Visual Basic would be a very convenient choice: It is widespread, and it does not require yet another license, since it is included in software tools that almost everyone has available. Such a choice would probably increase my royalties as well. To the very least, it can be considered a good language for fast prototyping.

These considerations, as well as the introduction of new MATLAB toolboxes aimed a t financial applications, are the reasons why I am sticking to my original choice. I have received much appreciated feedback and encouragement from readers of the first edition of the book. Some pointed out typos, errors, and inaccuracies. As with the first edition, I plan to keep a web page containing the hopefully short list of errata and the hopefully long list of supplements, as well as the MATLAB code described in the book.

In some sense, crossroads may be disappointing, indeed. In this book, different paths cross, involving finance, numerical analysis, optimization theory, probability theory, Monte Carlo simulation, and partial differential equations.

It is not a point of departure, because although the prerequisites are fairly low, some level of mathematical maturity on the part of the reader is assumed.

It is not a point of arrival, as many relevant issues have been omitted, such as hedging exotic options and interest-rate derivatives. Hence, this is not a research monograph; it is a textbook for students.

On the one hand, students in Economics usually have little background in numerical methods and lack the ability to translate algorithmic concepts into a working program; on the other hand, students in Engineering do not see the potential application of quantitative methods to finance clearly. Although there is an increasing literature on high-level mathematics applied to financial engineering, and a few books illustrating how cookbook recipes may be applied to a wide variety of problems through use of a spreadsheet, I believe there is some need for a n intermediate-level book, both interesting t o practitioners and suitable for self-study.

I believe that students should: Acquire reasonably strong foundations in order to appreciate the issues behind the application of numerical methods Be able to translate and check ideas quickly in a computational environment Gain confidence in their ability to apply methods, even by carrying out the apparently pointless task of using relatively sophisticated tools to pricing a vanilla European option Be encouraged to pursue further study by tackling more advanced subjects, from both practical and theoretical perspectives The material covered in the book has been selected with these aims in mind.

I am afraid the book will not please statisticians, as no econometric model is developed; however, there is a wide and excellent literature on those topics, and I tried to come up with a complementary text book.

The text is interspersed with MATLAB snapshots and pieces of code, to make the material as lively as possible and of immediate use. MATLAB is a flexible high-level computing environment which allows us to implement nontrivial algorithms with a few lines of code. It has also been chosen because of its increasing potential for specific financial applications.

It may be argued that the book is more successful at raising questions than at giving answers. This is a necessary evil, given the space available to cover such a wide array of topics. But if, after reading this book, students will want to read others, my job will have been accomplished. Sumit Kumar rated it it was amazing Dec 06, Yeki Vidal rated it it was amazing May 05, Sumit rated it really liked it Apr 03, Dk rated it it was amazing Jun 26, Columbus Saikhom rated it liked it Sep 01, Basavaraj Nelogal rated it liked it Feb 24, Danish Abrar rated it really liked it Feb 07, Darin rated it really liked it Mar 30, Farman rated it did not like it Feb 15, Banuvathy rated it really liked it Jul 12, Jameson added it Oct 16, Eren Sahin marked it as to-read Sep 22, Floietoss added it Mar 30, Rachel added it Jul 19, Mike added it Mar 03, Rex added it Jul 04, Erick Martinez marked it as to-read Sep 08, Huido marked it as to-read Sep 08, Pappu marked it as to-read Jul 23, Constantinos Karakannas marked it as to-read Oct 31, Irene added it Nov 01, Manu Prabhakar added it Feb 28, Randall Marrett marked it as to-read Apr 25, Monika Bhattacharya marked it as to-read Jul 20, Kiran Meena marked it as to-read Sep 24, Suleyman marked it as to-read Oct 09, Adnan Pasha is currently reading it Oct 24, Denton Sagerman marked it as to-read Nov 06, Sandeep Sandy marked it as to-read Dec 24, Gopal Kumar marked it as to-read Jan 12, Mustafa marked it as to-read Jan 17, Deepnarayan marked it as to-read Jan 31, Taufik marked it as to-read Feb 08, Mohammadmahdi added it Feb 29, Hasok marked it as to-read Aug 21, Ankit Bhinde marked it as to-read Oct 14, Salwan marked it as to-read Oct 30,