Brandimarte - Handbook in Monte Carlo Simulation

Handbook in Monte Carlo Simulation

Copyright 2014 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.
Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Brandimarte, Paolo.
Handbook in Monte Carlo simulation : applications in financial engineering, risk management, and economics / Paolo Brandimarte.
pages cm
Includes bibliographical references and index.
ISBN 978-0-470-53111-2 (cloth)
1. FinanceMathematical models. 2. EconomicsMathematical models. 3. Monte Carlo method. I. Title. HG106.B735 2014
330.01518282dc23
2013047832

Preface

The aim of this book is to provide a wide class of readers with a low- to intermediate-level treatment of Monte Carlo methods for applications in finance and economics. The target audience consists of students and junior practitioners with a quantitative background, and it includes not only students in economics and finance, but also in mathematics, statistics, and engineering. In fact, this is the kind of audience I typically deal with in my courses. Not all of these readers have a strong background in either statistics, financial economics, or econometrics, which is why I have also included some basic material on stochastic modeling in the early chapters, which is typically skipped in higher level books. Clearly, this is not meant as a substitute for a proper treatment, which can be found in the references listed at the end of each chapter. Some level of mathematical maturity is assumed, but the prerequisites are rather low and boil down to the essentials of probability and statistics, as well as some basic programming skills. Advanced readers may skip the introductory chapters on modeling and estimation, which are also included as a reminder that no Monte Carlo method, however sophisticated, will yield useful results if the input model is flawed. Indeed, the power and flexibility of such methods may lure us into a false sense of security, making us forget some of their inherent limitations.

Option pricing is certainly a relevant application domain for the techniques we discuss in the book, but this is not meant to be a book on financial engineering. I have also included a significant amount of material on optimization in its many guises, as well as a chapter related to computational Bayesian statistics. I have favored a wide scope over a deeply technical treatment, for which there are already some really excellent and more demanding books. Many of them, however, do not quite help the reader to really feel what she is learning, as no ready-to-use code is offered. In order to allow anyone to run the code, play with it, and hopefully come up with some variations on the theme, I have chosen to develop code in R. Readers familiar with my previous book written in MATLAB might wonder whether I have changed my mind. I did not: I never use R in research or consulting, but I use it a lot for teaching. When I started writing the book, I was less than impressed by the lack of an adequate development environment, and some design choices of the language itself left me a bit puzzled. As an example, the * operator in MATLAB multiplies matrices row by column; whenever you want to work elementwise, you use the . operator, which has a clear and uniform meaning when applied to other operators. On the contrary, the operator * works elementwise in R, and row-by-column matrix product is accomplished by the somewhat baroque operator %*%. Furthermore, having to desperately google every time you have to understand a command, because documentation is a bit poor and you have to make your way in a mess of packages, may be quite frustrating at times. I have also found that some optimization functions are less accurate and less clever in dealing with limit cases than the corresponding MATLAB functions. Having said that, while working on the book, I have started to appreciate R much more. Also my teaching experience with R has certainly been fun and rewarding. A free tool with such a potential as R is certainly most welcome, and R developers must be praised for offering all of this. Hopefully, the reader will find R code useful as a starting point for further experimentation. I did not assemble R code into a package, as this would be extremely misleading: I had no plan to develop an integrated and reliable set of functions. I just use R code to illustrate ideas in concrete terms and to encourage active learning. When appropriate, I have pointed out some programming practices that may help in reducing the computational burden, but as a general rule I have tried to emphasize clarity over efficiency. I have also avoided writing an introduction to R programming, as there are many freely available tutorials (and a few good books). A reader with some programming experience in any language should be able to make her way through the code, which has been commented on when necessary. My assumption is that a reader, when stumbling upon an unknown function, will take advantage of the online help and the example I provide in order to understand its use and potentiality. Typically, R library functions are equipped with optional parameters that can be put to good use, but for the sake of conciseness I have refrained from a full description of function inputs.

The book is organized in five parts.