Stochastic Simulation and Applications In

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

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).

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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Stochastic Simulation and Applications In Finance with MATLAB Programs

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