Monte Carlo Simulation and Finance

Praise for MONTE CARLO SIMULATION & FINANCE

"Dr. McLeish's clear exposition of simulation methods and their application to a wide variety of practical financial problems, along with the enlightening exercise problems, make this text perfectly suited for use at both the senior undergraduate and graduate levels. As a reference, this refreshing volume will be a handy aid for researchers and practitioners in constructing complex financial simulations and in using sound, statistical techniques to evaluate the output. This book is a valuable and important contribution to an increasingly vital area of quantitative finance."
—R. Mark Reesor, SHARCNet Research Chair in Financial Mathematics Department of Applied Mathematics, University of Western Ontario

"This book fills an important niche in a rapidly growing and very topical subject area. Both teachable and highly readable, this book is pitched at just the right level for anyone seeking to learn about this subject. The thoughtful choice of topics covered is greatly enhanced by very useful sets of exercises appearing at the back of each chapter."
—Andrey Feuerverger, Professor of Statistics and Instructor in the Mathematical Finance Program University of Toronto

"Excellent source of information on topics rarely covered elsewhere. The book not only explicates Monte Carlo techniques but also is full of stimulating insights that reflect the wealth of experience Don McLeish has in statistical methods."
—Adam Kolkiewicz, Associate Professor Department of Statistics and Actuarial Science, University of Waterloo

"The advanced theory of finance, like many other areas in which complex mathematics plays an important part, is undergoing a revolution aided by the computer and the proliferation of powerful simulation and symbolic mathematical tools. This is the mathematical equivalent of the invention of the printing press. The numerical and computational power once reserved for the most highly trained mathematicians, scientists, and engineers is now available to any competent programmer. "

—From Chapter 1

Monte Carlo simulation methods are among the most powerful and broadly applicable tools available for valuing derivatives and other financial securities. Recent exponential increases in the power and speed of computers have greatly expanded the scope, efficiency, and accuracy of Monte Carlo simulations, leading to the need for a comprehensive and thoroughly updated reference on the use of Monte Carlo techniques for financial engineering and modeling.

Monte Carlo Simulation and Finance provides financial engineers, researchers, and students with today's most detailed and application-based examination of Monte Carlo modeling techniques. Filled with valuable insights and methodologies for formulating the problem at hand; setting specific objectives; choosing and implementing the most applicable model; determining parameters; running the simulation; and documenting results and conclusions in light of the simulation results, the book features:

• Techniques for using performance measures to calibrate a simulation model
• Methodologies for addressing survivorship bias
• Variance reduction in simulation
• Importance sampling and pricing exotic options, including Asian options and Barrier options
• Pricing options under alternative, more realistic models
• Quasi–Monte Carlo multiple integration methods, which often generate estimates superior to traditional Monte Carlo methods
• Examples of van der Corput, Halton, Faure, and Sobol low-discrepancy sequences
• Chapter-ending problems that both test newly acquired knowledge and suggest avenues for further exploration
• An insightful discussion of the future of Monte Carlo financial simulation

Monte Carlo Simulation and Finance is an essential reference for anyone, professional or academic, looking to design and implement accurate models for securities pricing and risk management. Further theoretical and mathematical information supporting theconcepts discussed throughout this book also appear in an online appendix at www.wiley.com/go/mcleish. Today's most up-to-date and results-based guide to this vital area, Monte Carlo Simulation and Finance is certain to set the standard for Monte Carlo reference texts throughout the remainder of this decade.

DON L. McLEISH is Professor of Statistics and Actuarial Science at the University of Waterloo. His research has focused on probability, statistical methods and models in general, and their application to financial data, including wide-tail alternatives to the normal distribution and the consequences for derivatives and asset pricing. He has contributed to the application of Monte Carlo techniques, variance reduction, and stochastic calculus to problems in finance, and is cofounder of the University of Waterloo's Center for Advance Studies in Finance. McLeish is also coauthor, with C.G. Small, of The Theory and Application of Statistical Inference Functions and Hilbert Space Methods in Probability and Statistical Inference (Wiley).