Monte Carlo Simulation with Applications to Finance

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.

Review of Probability. Brownian Motion. Arbitrage Free Pricing. Monte Carlo Simulation. Generating Random Variables. Variance Reduction Techniques. Importance Sampling. Stochastic Calculus. Simulation of Diffusions. Sensitivity Analysis. Appendices. Bibliography. Index.

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.