Monte Carlo Simulation with Applications to Finance
By Hui Wang
Chapman and Hall/CRC – 2012 – 292 pages
Developed from the author’s course on Monte Carlo simulation at Brown University, Monte Carlo Simulation with Applications to Finance provides a self-contained introduction to Monte Carlo methods in financial engineering. It is suitable for advanced undergraduate and graduate students taking a one-semester course or for practitioners in the financial industry.
The author first presents the necessary mathematical tools for simulation, arbitrary free option pricing, and the basic implementation of Monte Carlo schemes. He then describes variance reduction techniques, including control variates, stratification, conditioning, importance sampling, and cross-entropy. The text concludes with stochastic calculus and the simulation of diffusion processes.
Only requiring some familiarity with probability and statistics, the book keeps much of the mathematics at an informal level and avoids technical measure-theoretic jargon to provide a practical understanding of the basics. It includes a large number of examples as well as MATLAB® coding exercises that are designed in a progressive manner so that no prior experience with MATLAB is needed.
"I liked this book because it gave me a good review of the mathematics of option pricing. The chapters are well written and were clear to me."
—INFORMS Journal on Computing, 25(1), 2013
"… is suitable for the practitioner in search of a hands-on approach to the topic, as well as the student/researcher who wants to have a quick way to know what simulation techniques (in particular for pricing derivatives) are about."
—Gunther Leobacher, Mathematical Reviews Clippings December 2013
Review of Probability
Independence and Conditional Probability
Classical Limit Theorems
Running Maximum of Brownian Motion
Derivatives and Black–Scholes Prices
Multidimensional Brownian Motions
Arbitrage Free Pricing
Arbitrage Free Principle
Asset Pricing with Binomial Trees
The Black–Scholes Model
Monte Carlo Simulation
Basics of Monte Carlo Simulation
Standard Error and Confidence Interval
Examples of Monte Carlo Simulation
Generating Random Variables
Inverse Transform Method
Sampling from Multivariate Normal Distributions
Variance Reduction Techniques
Basic Ideas of Importance Sampling
The Cross-Entropy Method
Applications to Risk Analysis
Stochastic Differential Equations
Simulation of Diffusions
Eliminating Discretization Error
Refinements of Euler Scheme
The Lamperti Transform
Commonly Used Greeks
Monte Carlo Simulation of Greeks
Appendix A: Multivariate Normal Distributions
Appendix B: American Option Pricing
Appendix C: Option Pricing Formulas
Exercises appear at the end of each chapter.
Hui Wang is an associate professor in the Division of Applied Mathematics at Brown University. He earned a Ph.D. in statistics from Columbia University. His research and teaching cover Monte Carlo simulation, mathematical finance, probability and statistics, and stochastic optimization.