Monte Carlo simulation with applications to finance

This book can serve as the text for a one-semester course on Monte Carlo simulation. The intended audience is advanced undergraduate students or students on master's programs who wish to learn the basics of this exciting topic and its applications to finance. The book is largely self-contained. The only prerequisite is some experience with probability and statistics. Prior knowledge on option pricing is helpful but not essential. As in any study of Monte Carlo simulation, coding is an integral part and cannot be ignored. The book contains a large number of MATLAB coding exercises. They are designed in a progressive manner so that no prior experience with MATLAB is required. Much of the mathematics in the book is informal. For example, randomvariables are simply defined to be functions on the sample space, even though they should be measurable with respect to appropriate algebras; exchanging the order of integrations is carried out liberally, even though it should be justified by the Tonelli-Fubini Theorem. The motivation for doing so is to avoid the technical measure theoretic jargon, which is of little concern in practice and does not help much to further the understanding of the topic. The book is an extension of the lecture notes that I have developed for an undergraduate course on Monte Carlo simulation at Brown University. I would like to thank the students who have taken the course, as well as the Division of Applied Mathematics at Brown, for their support. Hui Wang Providence, Rhode Island January, 2012.