Stochastic Simulation and Applications in Finance with MATLAB Programs / Edition 1

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Overview

This book is a good companion to text books on theory, soif you want to get straight to the meat of implementing theclassical quantitative finance models here's the answer.

—Paul Wilmott, wilmott.com

This powerful book is a comprehensive guide for MonteCarlo methods in finance. Every quant knows that one of the biggestissues in finance is to well understand the mathematical frameworkin order to translate it in programming code. Look at the chapteron Quasi Monte Carlo or the paragraph on variance reductiontechniques and you will see that Huu Tue Huynh, Van Son Lai andIssouf Soumaré have done a very good job in order to provide abridge between the complex mathematics used in finance and theprogramming implementation. Because it adopts both theoretical andpractical point of views with a lot of applications, because ittreats about some sophisticated financial problems (like Brownianbridges, jump processes, exotic options pricing orLongstaff-Schwartz methods) and because it is easy to understand,this handbook is valuable for academics, students and financialengineers who want to learn the computational aspects ofsimulations in finance.

—Thierry Roncalli, Head of Investment Products andStrategies, SGAM Alternative Investments & Professor ofFinance, University of Evry

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Product Details

  • ISBN-13: 9780470725382
  • Publisher: Wiley
  • Publication date: 12/30/2008
  • Series: Wiley Finance Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 6.60 (w) x 9.70 (h) x 1.30 (d)

Meet the Author

HUU TUE HUYNH obtained his D.Sc. in communication theoryfrom Laval University, Canada. From 1969 to 2004 he was a facultymember of Laval University. He left Laval University to becomeChairman of the Department of data processing at the College ofTechnology of The Vietnam National University, Hanoi. Since 2007 hehas been Rector of the Bac Ha International University, Vietnam.His main recent research interest covers Fast Monte Carlo methodsand applications.

VAN SON LAI is Professor of Finance at the BusinessSchool of Laval University, Canada. He obtained his Ph.D. inFinance from the University of Georgia, USA and a master degree inwater resources engineering from the University of BritishColumbia, Canada. He is also a CFA charterholder from the CFAInstitute and a registered P.Eng. in the Province of BritishColumbia. An established teacher and researcher in banking,financial engineering, and risk management, he has extensivelypublished in mainstream banking, economics, and financejournals.

ISSOUF SOUMARÉ is currently associate professor offinance and managing director of the Laboratory for FinancialEngineering at Laval University. His research and teachinginterests included risk management, financial engineering andnumerical methods in finance. He has published his theoretical andapplied finance works in economics and finance journals. DrSoumaré holds a PhD in Finance from the University of BritishColumbia, Canada, MSc in Financial Engineering from LavalUniversity, Canada, MSc in Statistics and Quantitative Economicsand MSc and BSc in Applied Mathematics from Ivory Coast. He is alsoa certified Professional Risk Manager (PRM) of the ProfessionalRisk Managers’ International Association (PRMIA).

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Table of Contents

Contents

Preface

1 Introduction to Probability

1.1 Intuitive Explanation

1.2 Axiomatic Definition

2 Introduction to Random Variables

2.1 Random Variables

2.2 Random Vectors

2.3 Transformation of Random Variables

2.4 Transformation of Random Vectors

2.5 Approximation of the Standard Normal Cumulative DistributionFunction

3 Random Sequences

3.1 Sum of Independent Random Variables

3.2 Law of Large Numbers

3.3 Central Limit Theorem

3.4 Convergence of Sequences of Random Variables

4 Introduction to Computer Simulation of RandomVariables

4.1 Uniform Random Variable Generator

4.2 Generating Discrete Random Variables

4.3 Simulation of Continuous Random Variables

4.4 Simulation of Random Vectors

4.5 Acceptance-Rejection Method

4.6 Markov Chain Monte Carlo Method (MCMC)

5 Foundations of Monte Carlo Simulations

5.1 Basic Idea

5.2 Introduction to the Concept of Precision

5.3 Quality of Monte Carlo Simulations Results

5.4 Improvement of the Quality of Monte Carlo Simulations orVariance Reduction Techniques

5.5 Application Cases of Random Variables Simulations

6 Fundamentals of Quasi Monte Carlo (QMC) Simulations

6.1 Van Der Corput Sequence (Basic Sequence)

6.2 Halton Sequence

6.3 Faure Sequence

6.4 Sobol Sequence

6.5 Latin Hypercube Sampling

6.6 Comparison of the Different Sequences

7 Introduction to Random Processes

7.1 Characterization

7.2 Notion of Continuity, Differentiability andIntegrability

7.3 Examples of Random Processes

8 Solution of Stochastic Differential Equations

8.1 Introduction to Stochastic Calculus

8.2 Introduction to Stochastic Differential Equations

8.3 Introduction to Stochastic Processes with Jump

8.4 Numerical Solutions of some Stochastic DifferentialEquations (SDE)

8.5 Application case: Generation of a Stochastic DifferentialEquation using the Euler and Milstein Schemes

8.6 Application Case: Simulation of a Stochastic DifferentialEquation with Control and Antithetic Variables

8.7 Application Case: Generation of a Stochastic DifferentialEquation with Jumps

9 General Approach to the Valuation of ContingentClaims

9.1 The Cox, Ross and Rubinstein (1979) Binomial Model of OptionPricing

9.2 Black and Scholes (1973) and Merton (1973) Option PricingModel

9.3 Derivation of the Black-Scholes Formula using theRisk-Neutral Valuation Principle

10 Pricing Options using Monte Carlo Simulations

10.1 Plain Vanilla Options: European put and Call

10.2 American options

10.3 Asian options

10.4 Barrier options

10.5 Estimation Methods for the Sensitivity Coefficients orGreeks

11 Term Structure of Interest Rates and Interest RateDerivatives

11.1 General Approach and the Vasicek (1977) Model

11.2 The General Equilibrium Approach: The Cox, Ingersoll andRoss (CIR, 1985) model

11.3 The Affine Model of the Term Structure

11.4 Market Models

12 Credit Risk and the Valuation of CorporateSecurities

12.1 Valuation of Corporate Risky Debts: The Merton (1974)Model

12.2 Insuring Debt Against Default Risk

12.3 Valuation of a Risky Debt: The Reduced-Form Approach

13 Valuation of Portfolios of Financial Guarantees

13.1 Valuation of a Portfolio of Loan Guarantees

13.2 Valuation of Credit Insurance Portfolios using Monte CarloSimulations

14 Risk Management and Value at Risk (VaR)

14.1 Types of Financial Risks

14.2 Definition of the Value at Risk (VaR)

14.3 The Regulatory Environment of Basle

14.4 Approaches to compute VaR

14.5 Computing VaR by Monte Carlo Simulations

15 VaR and Principal Components Analysis (PCA)

15.1 Introduction to the Principal Components Analysis

15.2 Computing the VaR of a Bond Portfolio

Appendix A: Review of Mathematics

A.1 Matrices

A.1.1 Elementary Operations on Matrices

A.1.2 Vectors

A.1.3 Properties

A.1.4 Determinants of Matrices

A.2 Solution of a System of Linear Equations

A.3 Matrix Decomposition

A.4 Polynomial and Linear Approximation

A.5 Eigenvectors and Eigenvalues of a Matrix

Appendix B: MATLAB®Functions

References and Bibliography

Index

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