Stochastic Simulation and Applications In Finance with MATLAB Programs

by Huynh, Huu Tue; Lai, Van Son; Soumare, Issouf

• ISBN13: 9780470725382
• ISBN10: 0470725389
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-12-22
• Publisher: Wiley

Summary

Stochastic Simulation and Applications in Finance with Matlab Programs begins by covering the basics of probability and statistics, which are essential to the understanding the later chapters on random processes and computational simulation techniques, it then goes on to discuss Monte Carlo simulations. In addition to the most commonly used techniques, the authors also cover the latest developments such as Markov Chain Monte Carlo and importance sampling methods, which are not discussed in other texts. The final part of the book covers random processes, stochastic differential equations and Brownian Bridges. * Features CD-ROM with examples and programs relating to end of chapter tests and examples and includes accompanying simulation programs in Matlab - a leading programming language commonly used in industry and academia * Covers the latest stochastic processes including American Bermudan Swaps and Markov Chain processes, not covered in other literature * Features case studies and examples from the financial industry as well as test exercises * An in-depth, rigorous explanation of how to apply stochastic simulations to financial engineering problems * Each chapter starts with an introduction to the topic (assuming prior knowledge of linear algebra, differential calculus and programming) taking the reader through to the most advanced elements of each topic

Author Biography

HUU TUE HUYNH obtained his D.Sc. in communication theory from Laval University, Canada. From 1969 to 2004 he was a faculty member of Laval University. He left Laval University to become Chairman of the Department of data processing at the College of Technology of The Vietnam National University, Hanoi. Since 2007 he has been Rector of the Bac Ha International University, Vietnam. His main recent research interest covers Fast Monte Carlo methods and applications.

VAN SON LAI is Professor of Finance at the Business School of Laval University, Canada. He obtained his Ph.D. in Finance from the University of Georgia, USA and a master degree in water resources engineering from the University of British Columbia, Canada. He is also a CFA charterholder from the CFA Institute and a registered P.Eng. in the Province of British Columbia. An established teacher and researcher in banking, financial engineering, and risk management, he has extensively published in mainstream banking, economics, and finance journals.

ISSOUF SOUMARÉ is currently associate professor of finance and managing director of the Laboratory for Financial Engineering at Laval University. His research and teaching interests included risk management, financial engineering and numerical methods in finance. He has published his theoretical and applied finance works in economics and finance journals. Dr Soumaré holds a PhD in Finance from the University of British Columbia, Canada, MSc in Financial Engineering from Laval University, Canada, MSc in Statistics and Quantitative Economics and MSc and BSc in Applied Mathematics from Ivory Coast. He is also a certified Professional Risk Manager (PRM) of the Professional Risk Managers’ International Association (PRMIA).

Table of Contents

Contents

Preface

Introduction to Probability

Intuitive Explanation

Axiomatic Definition

Introduction to Random Variables

Random Variables

Random Vectors

Transformation of Random Variables

Transformation of Random Vectors

Approximation of the Standard Normal Cumulative Distribution Function

Random Sequences

Sum of Independent Random Variables

Law of Large Numbers

Central Limit Theorem

Convergence of Sequences of Random Variables

Introduction to Computer Simulation of Random Variables

Uniform Random Variable Generator

Generating Discrete Random Variables

Simulation of Continuous Random Variables

Simulation of Random Vectors

Acceptance-Rejection Method

Markov Chain Monte Carlo Method (MCMC)

Foundations of Monte Carlo Simulations

Basic Idea

Introduction to the Concept of Precision

Quality of Monte Carlo Simulations Results

Improvement of the Quality of Monte Carlo Simulations or Variance Reduction Techniques

Application Cases of Random Variables Simulations

Fundamentals of Quasi Monte Carlo (QMC) Simulations

Van Der Corput Sequence (Basic Sequence)

Halton Sequence

Faure Sequence

Sobol Sequence

Latin Hypercube Sampling

Comparison of the Different Sequences

Introduction to Random Processes

Characterization

Notion of Continuity, Differentiability and Integrability

Examples of Random Processes

Solution of Stochastic Differential Equations

Introduction to Stochastic Calculus

Introduction to Stochastic Differential Equations

Introduction to Stochastic Processes with Jump

Numerical Solutions of some Stochastic Differential Equations (SDE)

Application case: Generation of a Stochastic Differential Equation using the Euler and Milstein Schemes

Application Case: Simulation of a Stochastic Differential Equation with Control and Antithetic Variables

Application Case: Generation of a Stochastic Differential Equation with Jumps

General Approach to the Valuation of Contingent Claims

The Cox, Ross and Rubinstein (1979) Binomial Model of Option Pricing

Black and Scholes (1973) and Merton (1973) Option Pricing Model

Derivation of the Black-Scholes Formula using the Risk-Neutral Valuation Principle

Pricing Options using Monte Carlo Simulations

Plain Vanilla Options: European put and Call

American options

Asian options

Barrier options

Estimation Methods for the Sensitivity Coefficients or Greeks

Term Structure of Interest Rates and Interest Rate Derivatives

General Approach and the Vasicek (1977) Model

The General Equilibrium Approach: The Cox, Ingersoll and Ross (CIR, 1985) model

The Affine Model of the Term Structure

Market Models

Credit Risk and the Valuation of Corporate Securities

Valuation of Corporate Risky Debts: The Merton (197

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