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## Book 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.

2. Preface
4. Acknowledgments
5. 1. Introduction
6. I. Fundamental Concepts
1. 2. Important Finance Concepts
1. 2.1. BASIC THEORY OF INTEREST
2. 2.2. ASSET CLASSES
1. 2.2.1. Equities
2. 2.2.2. Fixed Income Securities
1. 2.3.1. Borrowing Funds to Purchase Securities
2. 2.3.2. Long and Short Positions
4. 2.4. CALCULATING RATE OF RETURN
5. 2.5. VALUATION
6. 2.6. IMPORTANT CONCEPTS IN FIXED INCOME
1. 2.6.1. Spot Rates
2. 2.6.2. The Term Structure
3. 2.6.3. Forward Rates
5. 2.6.5. Duration
6. 2.6.6. Convexity
7. 2.6.7. Key Rate Duration
8. 2.6.8. Total Return
7. 2.7. SUMMARY
8. 2.8. NOTES
2. 3. Random Variables, Probability Distributions, and Important Statistical Concepts
1. 3.1. WHAT IS A PROBABILITY DISTRIBUTION?
2. 3.2. BERNOULLI PROBABILITY DISTRIBUTION AND PROBABILITY MASS FUNCTIONS
3. 3.3. BINOMIAL PROBABILITY DISTRIBUTION AND DISCRETE DISTRIBUTIONS
4. 3.4. NORMAL DISTRIBUTION AND PROBABILITY DENSITY FUNCTIONS
5. 3.5. CONCEPT OF CUMULATIVE PROBABILITY
6. 3.6. DESCRIBING DISTRIBUTIONS
1. 3.6.1. Measures of Central Tendency
2. 3.6.2. Measures of Risk
3. 3.6.3. Skew
4. 3.6.4. Kurtosis
7. 3.7. BRIEF OVERVIEW OF SOME IMPORTANT PROBABILITY DISTRIBUTIONS
1. 3.7.1. Discrete Distributions
2. 3.7.2. Continuous Distributions
8. 3.8. DEPENDENCE BETWEEN TWO RANDOM VARIABLES: COVARIANCE AND CORRELATION
9. 3.9. SUMS OF RANDOM VARIABLES
10. 3.10. JOINT PROBABILITY DISTRIBUTIONS AND CONDITIONAL PROBABILITY
11. 3.11. FROM PROBABILITY THEORY TO STATISTICAL MEASUREMENT: PROBABILITY DISTRIBUTIONS AND SAMPLING
12. 3.12. SUMMARY
13. 3.13. SOFTWARE HINTS
1. 3.13.1. @RISK
2. 3.13.2. MATLAB
14. 3.14. NOTES
3. 4. Simulation Modeling
1. 4.1. MONTE CARLO SIMULATION: A SIMPLE EXAMPLE
2. 4.2. WHY USE SIMULATION?
3. 4.3. IMPORTANT QUESTIONS IN SIMULATION MODELING
4. 4.4. RANDOM NUMBER GENERATION
1. 4.4.1. Inverse Transform Method
2. 4.4.2. What Defines a "Good" Random Number Generator?
3. 4.4.3. Pseudorandom Number Generators
4. 4.4.4. Quasirandom (Low-Discrepancy) Sequences
5. 4.4.5. Stratified Sampling
5. 4.5. SUMMARY
6. 4.6. SOFTWARE HINTS
1. 4.6.1. @RISK
2. 4.6.2. MATLAB
7. 4.7. NOTES
4. 5. Optimization Modeling
1. 5.1. OPTIMIZATION FORMULATIONS
2. 5.2. IMPORTANT TYPES OF OPTIMIZATION PROBLEMS
3. 5.3. OPTIMIZATION PROBLEM FORMULATION EXAMPLES
4. 5.4. OPTIMIZATION ALGORITHMS
5. 5.5. OPTIMIZATION DUALITY
6. 5.6. MULTISTAGE OPTIMIZATION
1. 5.6.1. Finite State Space
2. 5.6.2. Infinite State Space
3. 5.6.3. Steps in Formulating Multistage Optimization Problems
7. 5.7. OPTIMIZATION SOFTWARE
8. 5.8. SUMMARY
9. 5.9. SOFTWARE HINTS
1. 5.9.1. Excel Solver
3. 5.9.3. MATLAB's Optimization Toolbox
10. 5.10. NOTES
5. 6. Optimization under Uncertainty
1. 6.1. DYNAMIC PROGRAMMING
2. 6.2. STOCHASTIC PROGRAMMING
3. 6.3. ROBUST OPTIMIZATION
4. 6.4. SUMMARY
5. 6.5. NOTES
7. II. Portfolio Optimization and Risk Measures
1. 7. Asset Diversification and Efficient Frontiers
1. 7.1. THE CASE FOR DIVERSIFICATION
2. 7.2. THE CLASSICAL MEAN-VARIANCE OPTIMIZATION FRAMEWORK
3. 7.3. EFFICIENT FRONTIERS
4. 7.4. ALTERNATIVE FORMULATIONS OF THE CLASSICAL MEAN-VARIANCE OPTIMIZATION PROBLEM
5. 7.5. THE CAPITAL MARKET LINE
6. 7.6. EXPECTED UTILITY THEORY
7. 7.7. SUMMARY
8. 7.8. SOFTWARE HINTS
1. 7.8.1. Excel
2. 7.8.2. MATLAB
9. 7.9. NOTES
2. 8. Advances in the Theory of Portfolio Risk Measures
1. 8.1. CLASSES OF RISK MEASURES
1. 8.1.1. Dispersion Risk Measures
2. 8.1.2. Downside Risk Measures
2. 8.2. VALUE-AT-RISK
3. 8.3. CONDITIONAL VALUE-AT-RISK AND THE CONCEPT OF COHERENT RISK MEASURES
4. 8.4. SUMMARY
5. 8.5. SOFTWARE HINTS
1. 8.5.1. Excel/Palisade Decision Tools Suite
2. 8.5.2. MATLAB
6. 8.6. NOTES
3. 9. Equity Portfolio Selection in Practice
1. 9.1. THE INVESTMENT PROCESS
1. 9.1.1. Setting Investment Objectives
2. 9.1.2. Developing and Implementing a Portfolio Strategy
3. 9.1.3. Monitoring the Portfolio
2. 9.2. PORTFOLIO CONSTRAINTS COMMONLY USED IN PRACTICE
3. 9.3. BENCHMARK EXPOSURE AND TRACKING ERROR MINIMIZATION
4. 9.4. INCORPORATING TRANSACTION COSTS
5. 9.5. INCORPORATING TAXES
6. 9.6. MULTIACCOUNT OPTIMIZATION
7. 9.7. ROBUST PARAMETER ESTIMATION
8. 9.8. PORTFOLIO RESAMPLING
9. 9.9. ROBUST PORTFOLIO OPTIMIZATION
10. 9.10. SUMMARY
11. 9.11. SOFTWARE HINTS
1. 9.11.1. Excel Solver
2. 9.11.2. Palisades Decision Tools Suite (Evolver)
3. 9.11.3. MATLAB
12. 9.12. NOTES
4. 10. Fixed Income Portfolio Management in Practice
1. 10.1. MEASURING BOND PORTFOLIO RISK
2. 10.2. THE SPECTRUM OF BOND PORTFOLIO MANAGEMENT STRATEGIES
1. 10.2.1. Bond Market Indices
2. 10.2.2. Pure Bond Indexing Strategy
3. 10.2.3. Enhanced Indexing/Matching Primary Risk Factors Approach
4. 10.2.4. Enhanced Indexing/Minor Risk Factor Mismatches
5. 10.2.5. Active Management/Larger Risk Factor Mismatches
6. 10.2.6. Active Management/Full-Blown Active
7. 10.2.7. Using Quantitative Methods for Portfolio Allocation
3. 10.3. LIABILITY-DRIVEN STRATEGIES
1. 10.3.1. Immunization Strategy for a Single-Period Liability
2. 10.3.2. Cash Flow Matching Strategy
4. 10.4. SUMMARY
5. 10.5. NOTES
8. III. Asset Pricing Models
1. 11. Factor Models
1. 11.1. THE CAPITAL ASSET PRICING MODEL
2. 11.2. THE ARBITRAGE PRICING THEORY
3. 11.3. BUILDING MULTIFACTOR MODELS IN PRACTICE
4. 11.4. APPLICATIONS OF FACTOR MODELS IN PORTFOLIO MANAGEMENT
5. 11.5. SUMMARY
6. 11.6. SOFTWARE HINTS
7. 11.7. NOTES
2. 12. Modeling Asset Price Dynamics
1. 12.1. BINOMIAL TREES
2. 12.2. ARITHMETIC RANDOM WALKS
3. 12.3. GEOMETRIC RANDOM WALKS
4. 12.4. MEAN REVERSION
5. 12.5. ADVANCED RANDOM WALK MODELS
6. 12.6. STOCHASTIC PROCESSES
7. 12.7. SUMMARY
8. 12.8. SOFTWARE HINTS
1. 12.8.1. @RISK
2. 12.8.2. MATLAB
9. 12.9. NOTES
9. IV. Derivative Pricing and Use
1. 13. Introduction to Derivatives
1. 13.1. BASIC TYPES OF DERIVATIVES
1. 13.1.1. Forwards and Futures
2. 13.1.2. Options
3. 13.1.3. Swaps
2. 13.2. IMPORTANT CONCEPTS FOR DERIVATIVE PRICING AND USE
3. 13.3. PRICING FORWARDS AND FUTURES
4. 13.4. PRICING OPTIONS
1. 13.4.1. Using Binomial Trees to Price European Options
2. 13.4.2. The Black-Scholes Formula for European Options
3. 13.4.3. Pricing American Options with Binomial Trees
4. 13.4.4. Measuring Sensitivities
5. 13.5. PRICING SWAPS
6. 13.6. SUMMARY
7. 13.7. SOFTWARE HINTS
1. 13.7.1. Excel/VBA
2. 13.7.2. MATLAB
8. 13.8. NOTES
2. 14. Pricing Derivatives by Simulation
1. 14.1. COMPUTING OPTION PRICES WITH CRUDE MONTE CARLO SIMULATION
2. 14.2. VARIANCE REDUCTION TECHNIQUES
3. 14.3. QUASIRANDOM NUMBER SEQUENCES
4. 14.4. MORE SIMULATION APPLICATION EXAMPLES
1. 14.4.1. Pricing a Barrier Option
2. 14.4.2. Pricing an American Option
3. 14.4.3. Evaluating Greeks
4. 14.4.4. Examples of Pricing Interest Rate Derivatives
5. 14.5. SUMMARY
6. 14.6. SOFTWARE HINTS
1. 14.6.1. @RISK
2. 14.6.2. Visual Basic
3. 14.6.3. MATLAB
7. 14.7. NOTES
3. 15. Structuring and Pricing Residential Mortgage-Backed Securities
1. 15.1. TYPES OF ASSET-BACKED SECURITIES
2. 15.2. MORTGAGE-BACKED SECURITIES: IMPORTANT TERMINOLOGY
3. 15.3. TYPES OF RMBS STRUCTURES
1. 15.3.1. Agency Pass-Through RMBS
2. 15.3.2. Agency Stripped MBS
3. 15.3.3. Agency Collateralized Mortgage Obligations
4. 15.3.4. Private-Label RMBS
4. 15.4. PRICING RMBS BY SIMULATION
1. 15.4.1. Prepayment Models
2. 15.4.2. Interest Rate Models
3. 15.4.3. Putting It All Together
4. 15.4.4. Further Analysis
5. 15.4.5. Improving the Degree of Accuracy with Variance-Reduction Methods
5. 15.5. USING SIMULATION TO ESTIMATE SENSITIVITY OF RMBS PRICES TO DIFFERENT FACTORS
6. 15.6. STRUCTURING RMBS DEALS USING DYNAMIC PROGRAMMING
7. 15.7. SUMMARY
8. 15.8. NOTES
4. 16. Using Derivatives in Portfolio Management
1. 16.1. USING DERIVATIVES IN EQUITY PORTFOLIO MANAGEMENT
1. 16.1.1. Risk Management Strategies
2. 16.1.2. Return Enhancement Strategies
2. 16.2. USING DERIVATIVES IN BOND PORTFOLIO MANAGEMENT
1. 16.2.1. Controlling Interest Rate Risk
2. 16.2.2. Managing Credit Risk
3. 16.3. USING FUTURES TO IMPLEMENT AN ASSET ALLOCATION DECISION
4. 16.4. MEASURING PORTFOLIO RISK WHEN THE PORTFOLIO CONTAINS DERIVATIVES
5. 16.5. SUMMARY
6. 16.6. NOTES
10. V. Capital Budgeting Decisions
1. 17. Capital Budgeting under Uncertainty
1. 17.1. CLASSIFYING INVESTMENT PROJECTS
2. 17.2. INVESTMENT DECISIONS AND WEALTH MAXIMIZATION
3. 17.3. EVALUATING PROJECT RISK
1. 17.3.1. Measuring a Project's Market Risk
2. 17.3.2. Measuring a Project's Stand-Alone Risk
3. 17.3.3. Assessment of Project Risk in Practice
4. 17.4. CASE STUDY
1. 17.4.1.
1. 17.4.1.1. Rapid Bounce
2. 17.4.1.2. Persistence
2. 17.4.2. Computing the Cost of Capital
3. 17.4.3. Computing the NPV Profiles
4. 17.4.4. Running a Simulation to Estimate Project Stand-Alone Risk
5. 17.4.5. Determining the Inputs to the Simulation
5. 17.5. MANAGING PORTFOLIOS OF PROJECTS
6. 17.6. SUMMARY
7. 17.7. SOFTWARE HINTS
1. 17.7.1. @RISK
2. 17.7.2. MATLAB
8. 17.8. NOTES
2. 18. Real Options
1. 18.1. TYPES OF REAL OPTIONS
2. 18.2. REAL OPTIONS AND FINANCIAL OPTIONS
3. 18.3. NEW VIEW OF NPV
4. 18.4. OPTION TO EXPAND
5. 18.5. OPTION TO ABANDON
6. 18.6. MORE REAL OPTIONS EXAMPLES
7. 18.7. ESTIMATION OF INPUTS FOR REAL OPTION VALUATION MODELS
8. 18.8. SUMMARY
9. 18.9. SOFTWARE HINTS
10. 18.10. NOTES
3. References