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Simulation and Optimization in Finance Modeling with MATLAB
Contents
Preface xi
About the Authors xvi
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
vii
viii CONTENTS
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
Contents ix
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;
x CONTENTS
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