Wang Monte Carlo Simulation with Applications to Finance

1. Auflage 2012
ISBN: 978-1-4665-6690-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 292 Seiten

Reihe: Chapman & Hall/CRC Financial Mathematics Series

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.

Zielgruppe

Students in financial engineering, economics, and statistics.

Autoren/Hrsg.

Wang, Hui

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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
Summary

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

Bibliography
Index

Exercises appear at the end of each chapter.

Über Autor(innen)

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.