E-book

# Simulation and Optimization in Finance: Modeling with MATLAB, @Risk, or VBA

ISBN: 978-0-470-88212-2
896 pages
September 2010

## Description

An introduction to the theory and practice of financial simulation and optimization

In recent years, there has been a notable increase in the use of simulation and optimization methods in the financial industry. Applications include portfolio allocation, risk management, pricing, and capital budgeting under uncertainty.

This accessible guide provides an introduction to the simulation and optimization techniques most widely used in finance, while at the same time offering background on the financial concepts in these applications. In addition, it clarifies difficult concepts in traditional models of uncertainty in finance, and teaches you how to build models with software. It does this by reviewing current simulation and optimization methodology-along with available software-and proceeds with portfolio risk management, modeling of random processes, pricing of financial derivatives, and real options applications.

• Contains a unique combination of finance theory and rigorous mathematical modeling emphasizing a hands-on approach through implementation with software
• Highlights not only classical applications, but also more recent developments, such as pricing of mortgage-backed securities
• Includes models and code in both spreadsheet-based software (@RISK, Solver, Evolver, VBA) and mathematical modeling software (MATLAB)

Filled with in-depth insights and practical advice, Simulation and Optimization Modeling in Finance offers essential guidance on some of the most important topics in financial management.

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Preface xi

Acknowledgments xvii

CHAPTER 1 Introduction 1

Optimization; Simulation; Outline of Topics

PART ONE Fundamental Concepts

CHAPTER 2 Important Finance Concepts 11

Basic Theory of Interest; Asset Classes; Basic Trading Terminology; Calculating Rate of Return; Valuation;
Important Concepts in Fixed Income; Summary; Notes

CHAPTER 3 Random Variables, Probability Distributions, and Important Statistical Concepts 51

What is a Probability Distribution?; Bernoulli Probability Distribution and Probability Mass Functions; Binomial Probability Distribution and Discrete Distributions; Normal Distribution and Probability Density Functions; Concept of Cumulative Probability; Describing Distributions; Brief Overview of Some Important Probability Distributions; Dependence Between Two Random Variables: Covariance and Correlation; Sums of Random Variables; Joint Probability Distributions and Conditional Probability; From Probability Theory to Statistical Measurement: Probability Distributions and Sampling; Summary; Software Hints; Notes

CHAPTER 4 Simulation Modeling 101

Monte Carlo Simulation: A Simple Example; Why Use Simulation?; Important Questions in Simulation
Modeling; Random Number Generation; Summary; Software Hints; Notes

CHAPTER 5 Optimization Modeling 143

Optimization Formulations; Important Types of Optimization Problems; Optimization Problem Formulation Examples; Optimization Algorithms; Optimization Duality; Multistage Optimization; Optimization Software; Summary; Software Hints; Notes

CHAPTER 6 Optimization under Uncertainty 211

Dynamic Programming; Stochastic Programming; Robust Optimization; Summary; Notes

PART TWO Portfolio Optimization and Risk Measures

CHAPTER 7 Asset Diversification and Efficient Frontiers 245

The Case for Diversification; The Classical Mean-Variance Optimization Framework; Efficient Frontiers; Alternative Formulations of the Classical Mean-Variance Optimization Problem; The Capital Market Line; Expected Utility Theory; Summary; Software Hints; Notes

CHAPTER 8 Advances in the Theory of Portfolio Risk Measures 277

Classes of Risk Measures; Value-At-Risk; Conditional Value-At-Risk and the Concept of Coherent Risk
Measures; Summary; Software Hints; Notes

CHAPTER 9 Equity Portfolio Selection in Practice 321

The Investment Process; Portfolio Constraints Commonly Used in Practice; Benchmark Exposure and
Tracking Error Minimization; Incorporating Transaction Costs; Incorporating Taxes; Multiaccount
Optimization; Robust Parameter Estimation; Portfolio Resampling; Robust Portfolio Optimization; Summary;
Software Hints; Notes

CHAPTER 10 Fixed Income Portfolio Management in Practice 373

Measuring Bond Portfolio Risk; The Spectrum of Bond Portfolio Management Strategies; Liability-Driven
Strategies; Summary; Notes

PART THREE Asset Pricing Models

CHAPTER 11 Factor Models 401

The Capital Asset Pricing Model; The Arbitrage Pricing Theory; Building Multifactor Models in Practice;
Applications of Factor Models in Portfolio Management; Summary; Software Hints; Notes

CHAPTER 12 Modeling Asset Price Dynamics 421

Binomial Trees; Arithmetic Random Walks; Geometric Random Walks; Mean Reversion; Advanced Random
Walk Models; Stochastic Processes; Summary; Software Hints; Notes

PART FOUR Derivative Pricing and Use

CHAPTER 13 Introduction to Derivatives 477

Basic Types of Derivatives; Important Concepts for Derivative Pricing and Use; Pricing Forwards and
Futures; Pricing Options; Pricing Swaps; Summary; Software Hints; Notes

CHAPTER 14 Pricing Derivatives by Simulation 531

Computing Option Prices with Crude Monte Carlo Simulation; Variance Reduction Techniques;
Quasirandom Number Sequences; More Simulation Application Examples; Summary; Software Hints; Notes

CHAPTER 15 Structuring and Pricing Residential Mortgage-Backed Securities 587

Types of Asset-Backed Securities; Mortgage-Backed Securities: Important Terminology; Types of RMBS
Structures; Pricing RMBS by Simulation; Using Simulation to Estimate Sensitivity of RMBS Prices to Different Factors; Structuring RMBS Deals Using Dynamic Programming; Summary; Notes

CHAPTER 16 Using Derivatives in Portfolio Management 627

Using Derivatives in Equity Portfolio Management; Using Derivatives in Bond Portfolio Management;
Using Futures to Implement an Asset Allocation Decision; Measuring Portfolio Risk When the Portfolio
Contains Derivatives; Summary; Notes

PART FIVE Capital Budgeting Decisions

CHAPTER 17 Capital Budgeting under Uncertainty 653

Classifying Investment Projects; Investment Decisions and Wealth Maximization; Evaluating Project Risk;
Case Study; Managing Portfolios of Projects; Summary; Software Hints; Notes

CHAPTER 18 Real Options 707

Types of Real Options; Real Options and Financial Options; New View of NPV; Option to Expand; Option to
Abandon; More Real Options Examples; Estimation of Inputs for Real Option Valuation Models; Summary;  Software Hints; Notes

References 733

Index 743

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## Author Information

DESSISLAVA A. PACHAMANOVA, PhD, is an Associate Professor of Operations Research at Babson College where she holds the Zwerling Term Chair. She has published a number of articles in operations research, finance, and engineering journals, and co-authored the Wiley title Robust Portfolio Optimization and Management. Pachamanova's academic research is supplemented by consulting and previous work in the financial industry, including projects with quantitative strategy groups at WestLB and Goldman Sachs. She holds an AB in mathematics from Princeton University and a PhD in operations research from the Sloan School of Management at MIT.

Frank J. Fabozzi, PhD, CFA, CPA, is Professor in the Practice of Finance and Becton Fellow at theYale School of Management and Editor of the Journal of Portfolio Management. He is an Affiliated Professor at the University of Karlsruhe's Institute of Statistics, Econometrics, and Mathematical Finance and is on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University. He earned a doctorate in economics from the City University of New York.

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