Monte Carlo Simulation with Applications to Finance [Hardcover]

Developed from the authors course on Monte Carlo simulation at Brown University, Monte Carlo Simulation with Applications to Financeprovides 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
Probability Space
Independence and Conditional Probability
Random Variables
Random Vectors
Conditional Distributions
Conditional Expectation
Classical Limit Theorems

Brownian Motion
Brownian Motion
Running Maximum of Brownian Motion
Derivatives and BlackScholes Prices
Multidimensional Brownian Motions

Arbitrage Free Pricing
Arbitrage Free Principle
Asset Pricing with Binomial Trees
The BlackScholes Model

Monte Carlo Simulation