Monte Carlo Simulation with Applications to Finance: 1st Edition (Hardback) book cover

Monte Carlo Simulation with Applications to Finance

1st Edition

By Hui Wang

Chapman and Hall/CRC

292 pages | 22 B/W Illus.

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pub: 2012-05-22
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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

Table of Contents

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 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

Acceptance-Rejection Method

Sampling from Multivariate Normal Distributions

Variance Reduction Techniques

Antithetic Sampling

Control Variates

Stratified Sampling

Importance Sampling

Basic Ideas of Importance Sampling

The Cross-Entropy Method

Applications to Risk Analysis

Stochastic Calculus

Stochastic Integrals

Itô Formula

Stochastic Differential Equations

Risk-Neutral Pricing

Black–Scholes Equation

Simulation of Diffusions

Euler Scheme

Eliminating Discretization Error

Refinements of Euler Scheme

The Lamperti Transform

Numerical Examples

Sensitivity Analysis

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.

About the Author

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.

About the Series

Chapman and Hall/CRC Financial Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General