You are previewing Simulation and Optimization in Finance: Modeling with MATLAB, @RISK, or VBA.
O'Reilly logo
Simulation and Optimization in Finance: Modeling with MATLAB, @RISK, or VBA

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.

Table of Contents

  1. Copyright
  2. Preface
    1. CENTRAL THEMES
    2. SOFTWARE
    3. TEACHING
    4. COMPANION WEB SITE
    5. NOTES
  3. About the Authors
  4. Acknowledgments
  5. 1. Introduction
    1. 1.1. OPTIMIZATION
    2. 1.2. SIMULATION
    3. 1.3. OUTLINE OF TOPICS
  6. I. Fundamental Concepts
    1. 2. Important Finance Concepts
      1. 2.1. BASIC THEORY OF INTEREST
        1. 2.1.1. Compound Interest
        2. 2.1.2. Present Value and Future Value
      2. 2.2. ASSET CLASSES
        1. 2.2.1. Equities
        2. 2.2.2. Fixed Income Securities
          1. 2.2.2.1. Accrued Interest
          2. 2.2.2.2. Provisions for Paying Off Bonds
          3. 2.2.2.3. Conversion Privilege
          4. 2.2.2.4. Currency Denomination
          5. 2.2.2.5. Embedded Options
          6. 2.2.2.6. Credit Risk
      3. 2.3. BASIC TRADING TERMINOLOGY
        1. 2.3.1. Borrowing Funds to Purchase Securities
          1. 2.3.1.1. Margin Buying
          2. 2.3.1.2. Repurchase Agreement
        2. 2.3.2. Long and Short Positions
      4. 2.4. CALCULATING RATE OF RETURN
      5. 2.5. VALUATION
        1. 2.5.1. Valuation Models for Equities
        2. 2.5.2. Valuation Models for Fixed Income Securities
      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
        4. 2.6.4. Credit Spreads
        5. 2.6.5. Duration
          1. 2.6.5.1. Dollar Duration
          2. 2.6.5.2. Modified Duration, Macaulay Duration, and Effective Duration
          3. 2.6.5.3. Spread Duration for Fixed Rate Bonds
        6. 2.6.6. Convexity
          1. 2.6.6.1. Convexity Measure
          2. 2.6.6.2. Convexity Adjustment to Percentage Price Change
        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
          1. 3.6.1.1. Mean
          2. 3.6.1.2. Median
          3. 3.6.1.3. Mode
        2. 3.6.2. Measures of Risk
          1. 3.6.2.1. Variance and Standard Deviation
          2. 3.6.2.2. Coefficient of Variation
          3. 3.6.2.3. Range
          4. 3.6.2.4. Percentiles
        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
          1. 3.7.1.1. Discrete Uniform Distribution
          2. 3.7.1.2. Poisson Distribution
        2. 3.7.2. Continuous Distributions
          1. 3.7.2.1. Continuous Uniform Distribution
          2. 3.7.2.2. Triangular Distribution
          3. 3.7.2.3. Student's t-Distribution
          4. 3.7.2.4. Lognormal Distribution
          5. 3.7.2.5. Exponential Distribution
          6. 3.7.2.6. Chi-Square Distribution
          7. 3.7.2.7. Beta Distribution
      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
        1. 3.11.1. Central Limit Theorem
        2. 3.11.2. Confidence Intervals
        3. 3.11.3. Bootstrapping
        4. 3.11.4. Hypothesis Testing
      12. 3.12. SUMMARY
      13. 3.13. SOFTWARE HINTS
        1. 3.13.1. @RISK
        2. 3.13.2. MATLAB
          1. 3.13.2.1. Bernoulli Distribution
          2. 3.13.2.2. Binomial Distribution
          3. 3.13.2.3. Normal Distribution
          4. 3.13.2.4. Discrete Uniform Distribution
          5. 3.13.2.5. Continuous Uniform Distribution
          6. 3.13.2.6. Triangular Distribution
          7. 3.13.2.7. Student's t-Distribution
          8. 3.13.2.8. Lognormal Distribution
          9. 3.13.2.9. Exponential Distribution
          10. 3.13.2.10. Poisson Distribution
          11. 3.13.2.11. Chi-Square Distribution
          12. 3.13.2.12. Beta Distribution
      14. 3.14. NOTES
    3. 4. Simulation Modeling
      1. 4.1. MONTE CARLO SIMULATION: A SIMPLE EXAMPLE
        1. 4.1.1. Selecting Probability Distributions for the Inputs
        2. 4.1.2. Interpreting Monte Carlo Simulation Output
      2. 4.2. WHY USE SIMULATION?
        1. 4.2.1. Multiple Input Variables and Compounding Distributions
        2. 4.2.2. Incorporating Correlations
        3. 4.2.3. Evaluating Decisions
      3. 4.3. IMPORTANT QUESTIONS IN SIMULATION MODELING
        1. 4.3.1. How Many Scenarios?
        2. 4.3.2. Estimator Bias
        3. 4.3.3. Estimator Efficiency
      4. 4.4. RANDOM NUMBER GENERATION
        1. 4.4.1. Inverse Transform Method
          1. 4.4.1.1. The Inverse Transform for Discrete Distributions
          2. 4.4.1.2. The Inverse Transform for Continuous Distributions
        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
          1. 4.6.1.1. Example from Section 4.1.2
          2. 4.6.1.2. Example from Section 4.2.1
          3. 4.6.1.3. Example from Section 4.2.2
          4. 4.6.1.4. Example from Section 4.2.3
        2. 4.6.2. MATLAB
          1. 4.6.2.1. Example from Section 4.1.2
          2. 4.6.2.2. Example from Section 4.2.1
          3. 4.6.2.3. Example from Section 4.2.2
          4. 4.6.2.4. Example from Section 4.2.3
      7. 4.7. NOTES
    4. 5. Optimization Modeling
      1. 5.1. OPTIMIZATION FORMULATIONS
        1. 5.1.1. Minimization vs. Maximization
        2. 5.1.2. Local vs. Global Optima
        3. 5.1.3. Multiple Objectives
      2. 5.2. IMPORTANT TYPES OF OPTIMIZATION PROBLEMS
        1. 5.2.1. Convex Programming
        2. 5.2.2. Linear Programming
        3. 5.2.3. Quadratic Programming
        4. 5.2.4. Second-Order Cone Programming
        5. 5.2.5. Integer and Mixed Integer Programming
      3. 5.3. OPTIMIZATION PROBLEM FORMULATION EXAMPLES
        1. 5.3.1. Portfolio Allocation
        2. 5.3.2. Cash Flow Matching
        3. 5.3.3. Capital Budgeting
      4. 5.4. OPTIMIZATION ALGORITHMS
        1. 5.4.1. Linear Optimization: The Simplex Algorithm and Interior Point Methods
        2. 5.4.2. Constrained Nonlinear Optimization: The KKT Conditions and Lagrange Multipliers
        3. 5.4.3. Integer Programming Algorithms
        4. 5.4.4. Randomized Search Algorithms
        5. 5.4.5. Algorithm Efficiency
      5. 5.5. OPTIMIZATION DUALITY
      6. 5.6. MULTISTAGE OPTIMIZATION
        1. 5.6.1. Finite State Space
          1. 5.6.1.1. Standard Notation Used in Dynamic Programming
          2. 5.6.1.2. On the Relationship between Dynamic Programming and Classical Optimization Formulations
        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
          1. 5.9.1.1. Implementation of the Portfolio Allocation Example from Section 5.3.1
          2. 5.9.1.2. Implementation of the Capital Budgeting Example from Section 5.3.3
        2. 5.9.2. Palisade's Evolver
          1. 5.9.2.1. Implementation of the Portfolio Allocation Example from Section 5.3.1
          2. 5.9.2.2. Implementation of the Capital Budgeting Example from Section 5.3.3
        3. 5.9.3. MATLAB's Optimization Toolbox
          1. 5.9.3.1. Implementation of the Portfolio Allocation Example from Section 5.3.1
          2. 5.9.3.2. Implementation of the Capital Budgeting Example from Section 5.3.3
      10. 5.10. NOTES
    5. 6. Optimization under Uncertainty
      1. 6.1. DYNAMIC PROGRAMMING
      2. 6.2. STOCHASTIC PROGRAMMING
        1. 6.2.1. Multistage Models
        2. 6.2.2. Mean-Risk Stochastic Models
        3. 6.2.3. Chance-Constrained Models
      3. 6.3. ROBUST OPTIMIZATION
        1. 6.3.1. Uncertainty Sets and Robust Counterparts
        2. 6.3.2. Multistage 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
        1. 7.4.1. Expected Return Formulation
        2. 7.4.2. Risk Aversion Formulation
      5. 7.5. THE CAPITAL MARKET LINE
      6. 7.6. EXPECTED UTILITY THEORY
        1. 7.6.1. Quadratic Utility Function
        2. 7.6.2. Linear Utility Function
        3. 7.6.3. Exponential Utility Function
        4. 7.6.4. Power Utility Function
        5. 7.6.5. Logarithmic Utility Function
      7. 7.7. SUMMARY
      8. 7.8. SOFTWARE HINTS
        1. 7.8.1. Excel
          1. 7.8.1.1. Worksheet Setup
          2. 7.8.1.2. Using Excel Solver
          3. 7.8.1.3. Applying Array Functions
          4. 7.8.1.4. Calculating the Efficient Frontier with VBA
        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
          1. 8.1.1.1. Variance and Standard Deviation
          2. 8.1.1.2. Absolute Deviation
          3. 8.1.1.3. Absolute Moment
        2. 8.1.2. Downside Risk Measures
          1. 8.1.2.1. Lower-Partial Moment
          2. 8.1.2.2. Semivariance
          3. 8.1.2.3. Roy's Safety-First Criterion
          4. 8.1.2.4. Quantile-Based Risk Measures
      2. 8.2. VALUE-AT-RISK
        1. 8.2.1. The History of the Value-at-Risk Metric
        2. 8.2.2. Calculation of Value-at-Risk for a Normal Distribution
        3. 8.2.3. Calculation of Value-at-Risk Using Historical and Simulated Data Scenarios
        4. 8.2.4. VaR Calculation Example
        5. 8.2.5. Selection of Value-at-Risk Parameters and Regulatory Requirements
        6. 8.2.6. Optimization of Value-at-Risk
        7. 8.2.7. Arguments For and Against Value-at-Risk
      3. 8.3. CONDITIONAL VALUE-AT-RISK AND THE CONCEPT OF COHERENT RISK MEASURES
        1. 8.3.1. Estimation of Conditional Value-at-Risk from a Normal Distribution
        2. 8.3.2. Estimation of Conditional Value-at-Risk from a Discrete Distribution
        3. 8.3.3. Optimization of Conditional Value-at-Risk
      4. 8.4. SUMMARY
      5. 8.5. SOFTWARE HINTS
        1. 8.5.1. Excel/Palisade Decision Tools Suite
          1. 8.5.1.1. VaR Estimation
          2. 8.5.1.2. CVaR Estimation
          3. 8.5.1.3. VaR Optimization
          4. 8.5.1.4. CVaR Optimization
        2. 8.5.2. MATLAB
          1. 8.5.2.1. VaR and CVaR Estimation
          2. 8.5.2.2. VaR and CVaR Optimization
      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
          1. 9.1.2.1. Selecting the Type of Investment Strategy
          2. 9.1.2.2. Formulating the Inputs for Portfolio Construction
          3. 9.1.2.3. Constructing the Portfolio
        3. 9.1.3. Monitoring the Portfolio
        4. 9.1.4. Adjusting the Portfolio
      2. 9.2. PORTFOLIO CONSTRAINTS COMMONLY USED IN PRACTICE
        1. 9.2.1. Long-Only (No-Short-Selling) Constraints
        2. 9.2.2. Holding Constraints
        3. 9.2.3. Turnover Constraints
        4. 9.2.4. Risk Factor Constraints
        5. 9.2.5. Cardinality Constraints
        6. 9.2.6. Minimum Holding and Transaction Size Constraints
        7. 9.2.7. Round Lot Constraints
      3. 9.3. BENCHMARK EXPOSURE AND TRACKING ERROR MINIMIZATION
        1. 9.3.1. Standard Definition of Tracking Error
        2. 9.3.2. Alternative Ways of Defining Tracking Error
        3. 9.3.3. Actual vs. Predicted Tracking Error
      4. 9.4. INCORPORATING TRANSACTION COSTS
        1. 9.4.1. Linear Transaction Costs
        2. 9.4.2. Piecewise-Linear Transaction Costs
        3. 9.4.3. Quadratic Transaction Costs
        4. 9.4.4. Fixed 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
          1. 9.11.1.1. Limiting the Number of Stocks in the Portfolio
          2. 9.11.1.2. Index Tracking
        2. 9.11.2. Palisades Decision Tools Suite (Evolver)
          1. 9.11.2.1. Limiting the Number of Stocks in the Portfolio
          2. 9.11.2.2. Index Tracking
          3. 9.11.2.3. Limited Index Tracking
        3. 9.11.3. MATLAB
      12. 9.12. NOTES
    4. 10. Fixed Income Portfolio Management in Practice
      1. 10.1. MEASURING BOND PORTFOLIO RISK
        1. 10.1.1. Interest Rate Risk
        2. 10.1.2. Yield Curve Risk
        3. 10.1.3. Spread Risk
        4. 10.1.4. Credit Risk
        5. 10.1.5. Estimating Value-at-Risk for Fixed Income Securities
      2. 10.2. THE SPECTRUM OF BOND PORTFOLIO MANAGEMENT STRATEGIES
        1. 10.2.1. Bond Market Indices
          1. 10.2.1.1. Broad-Based Bond Market Indices
          2. 10.2.1.2. Specialized Bond Market Indices
          3. 10.2.1.3. International Bond 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
          1. 10.2.6.1. Interest Rate Expectations Strategies
          2. 10.2.6.2. Yield Curve Strategies
          3. 10.2.6.3. Inter- and Intrasector Allocation Strategies
          4. 10.2.6.4. Individual Security Selection Strategies
        7. 10.2.7. Using Quantitative Methods for Portfolio Allocation
          1. 10.2.7.1. Stratified Sampling Approach
          2. 10.2.7.2. Optimization Approach
      3. 10.3. LIABILITY-DRIVEN STRATEGIES
        1. 10.3.1. Immunization Strategy for a Single-Period Liability
          1. 10.3.1.1. A Simple Example
          2. 10.3.1.2. Further Issues
        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
        1. 11.3.1. Regression Analysis
        2. 11.3.2. Factor Analysis
        3. 11.3.3. Principal Components Analysis
      4. 11.4. APPLICATIONS OF FACTOR MODELS IN PORTFOLIO MANAGEMENT
        1. 11.4.1. Portfolio Performance Measurement
        2. 11.4.2. Risk Decomposition in Equity Portfolios
        3. 11.4.3. Efficient Mean-Variance Optimization
        4. 11.4.4. Risk Decomposition in Bond Portfolios
      5. 11.5. SUMMARY
      6. 11.6. SOFTWARE HINTS
        1. 11.6.1. Running a Regression with Excel
        2. 11.6.2. Running a Regression with MATLAB
      7. 11.7. NOTES
    2. 12. Modeling Asset Price Dynamics
      1. 12.1. BINOMIAL TREES
      2. 12.2. ARITHMETIC RANDOM WALKS
        1. 12.2.1. Simulation
        2. 12.2.2. Parameter Estimation
        3. 12.2.3. Arithmetic Random Walk: Some Additional Facts
      3. 12.3. GEOMETRIC RANDOM WALKS
        1. 12.3.1. Simulation
        2. 12.3.2. Parameter Estimation
        3. 12.3.3. Geometric Random Walk: Some Additional Facts
      4. 12.4. MEAN REVERSION
        1. 12.4.1. Simulation
        2. 12.4.2. Parameter Estimation
        3. 12.4.3. The Cox-Ingersoll-Ross Model for Interest Rates Dynamics
        4. 12.4.4. Geometric Mean Reversion
      5. 12.5. ADVANCED RANDOM WALK MODELS
        1. 12.5.1. Correlated Random Walks
        2. 12.5.2. Incorporating Jumps
        3. 12.5.3. Stochastic Volatility
      6. 12.6. STOCHASTIC PROCESSES
      7. 12.7. SUMMARY
      8. 12.8. SOFTWARE HINTS
        1. 12.8.1. @RISK
          1. 12.8.1.1. Arithmetic random walk
          2. 12.8.1.2. Geometric Random Walk
          3. 12.8.1.3. Mean Reversion
          4. 12.8.1.4. Geometric Mean Reversion
        2. 12.8.2. MATLAB
          1. 12.8.2.1. Arithmetic and Geometric Random Walks
          2. 12.8.2.2. Mean Reversion and Geometric Mean Reversion
      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
          1. 13.1.2.1. Buying a European Call Option (Long a Call Option)
          2. 13.1.2.2. Selling a Call Option (Short a Call Option)
          3. 13.1.2.3. Buying a Put Option (Long a Put Option)
          4. 13.1.2.4. Selling a Put Option (Short a Put Option)
        3. 13.1.3. Swaps
          1. 13.1.3.1. Equity Swaps
          2. 13.1.3.2. Interest Rate Swaps
          3. 13.1.3.3. Credit Default Swaps
      2. 13.2. IMPORTANT CONCEPTS FOR DERIVATIVE PRICING AND USE
        1. 13.2.1. Arbitrage
        2. 13.2.2. Hedging
      3. 13.3. PRICING FORWARDS AND FUTURES
      4. 13.4. PRICING OPTIONS
        1. 13.4.1. Using Binomial Trees to Price European Options
          1. 13.4.1.1. A Simple One-Period Example
          2. 13.4.1.2. Risk-Neutral Probabilities
          3. 13.4.1.3. Generalization to Multiple Periods
        2. 13.4.2. The Black-Scholes Formula for European Options
          1. 13.4.2.1. Estimating the Parameters in the Black-Scholes Formula
          2. 13.4.2.2. The Black-Scholes Option Pricing Formula and Geometric Random Walks
          3. 13.4.2.3. Relationship between the Black-Scholes Option Pricing Formula and the Binomial Tree Pricing Model
          4. 13.4.2.4. Matching Parameters
          5. 13.4.2.5. The Black-Scholes Formula and Bonds
        3. 13.4.3. Pricing American Options with Binomial Trees
        4. 13.4.4. Measuring Sensitivities
          1. 13.4.4.1. Delta
          2. 13.4.4.2. Gamma
          3. 13.4.4.3. Theta
          4. 13.4.4.4. Vega
      5. 13.5. PRICING SWAPS
      6. 13.6. SUMMARY
      7. 13.7. SOFTWARE HINTS
        1. 13.7.1. Excel/VBA
          1. 13.7.1.1. Bond Arbitrage Using Optimization
          2. 13.7.1.2. Implementing the Black-Scholes Formula with Excel
          3. 13.7.1.3. Implementing the Black-Scholes Formula with VBA
          4. 13.7.1.4. Finding the Black-Scholes Implied Volatility with Excel Solver
          5. 13.7.1.5. Finding the Black-Scholes Implied Volatility with VBA
          6. 13.7.1.6. American Option Pricing with the Binomial Method
        2. 13.7.2. MATLAB
          1. 13.7.2.1. Bond Arbitrage Using Optimization
          2. 13.7.2.2. Implementing the Black-Scholes Formula
          3. 13.7.2.3. Finding the Black-Scholes Implied Volatility
          4. 13.7.2.4. American Option Pricing with the Binomial Method
      8. 13.8. NOTES
    2. 14. Pricing Derivatives by Simulation
      1. 14.1. COMPUTING OPTION PRICES WITH CRUDE MONTE CARLO SIMULATION
        1. 14.1.1. Pricing a European Call Option by Simulation
        2. 14.1.2. Pricing an Asian Option by Simulation
      2. 14.2. VARIANCE REDUCTION TECHNIQUES
        1. 14.2.1. Antithetic Variables
        2. 14.2.2. Stratified Sampling
        3. 14.2.3. Importance Sampling
        4. 14.2.4. Control Variates
      3. 14.3. QUASIRANDOM NUMBER SEQUENCES
        1. 14.3.1. Van der Corput Sequence
        2. 14.3.2. Halton Sequence
        3. 14.3.3. Faure Sequence
        4. 14.3.4. Sobol Sequence
        5. 14.3.5. Illustrations
      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
          1. 14.4.4.1. Interest Rate Caps
          2. 14.4.4.2. Swaptions
      5. 14.5. SUMMARY
      6. 14.6. SOFTWARE HINTS
        1. 14.6.1. @RISK
          1. 14.6.1.1. Pricing a European Call Option
          2. 14.6.1.2. Pricing an Asian Call Option
        2. 14.6.2. Visual Basic
          1. 14.6.2.1. Pricing a European Call Option Using Crude Monte Carlo
          2. 14.6.2.2. Pricing an Asian Call Option with Crude Monte Carlo
          3. 14.6.2.3. Pricing a European Call Option with Antithetic Variables
          4. 14.6.2.4. Pricing an Asian Call Option with the Control Variates Method
          5. 14.6.2.5. Constructing a Van der Corput Quasirandom Sequence
          6. 14.6.2.6. Constructing a Halton Quasirandom Sequence
          7. 14.6.2.7. Computing the Price of a European Call Option with the Halton Sequence
          8. 14.6.2.8. Pricing a Down-and-Out Put Option with Crude Monte Carlo
          9. 14.6.2.9. Pricing an American Put Option with Regression Methods
          10. 14.6.2.10. Evaluating a European Call Option Delta with Naïve Monte Carlo and a Pathwise Method
        3. 14.6.3. MATLAB
          1. 14.6.3.1. Pricing a European Call Option Using Crude Monte Carlo
          2. 14.6.3.2. Pricing an Asian Call Option with Crude Monte Carlo
          3. 14.6.3.3. Pricing a European Call Option with Antithetic Variables
          4. 14.6.3.4. Pricing an Asian Call Option with the Control Variates Method
          5. 14.6.3.5. Constructing a Van der Corput Quasirandom Sequence
          6. 14.6.3.6. Constructing a Halton Quasirandom Sequence
          7. 14.6.3.7. Constructing a Sobol Quasirandom Sequence
          8. 14.6.3.8. Computing the Price of a European Call Option with the Halton or the Sobol Sequence
          9. 14.6.3.9. Pricing a Down-and-Out Put Option with Crude Monte Carlo
          10. 14.6.3.10. Pricing an American Put Option with Regression Methods
          11. 14.6.3.11. Evaluating a European Call Option Delta with Naïve Monte Carlo and a Pathwise Method
      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
        1. 15.2.1. Cash Flow Characteristics of a Residential Mortgage Loan
        2. 15.2.2. Prepayments and Cash Flow Uncertainty
        3. 15.2.3. Prepayments and Prepayment Conventions
        4. 15.2.4. Prepayments and Path Dependency
      3. 15.3. TYPES OF RMBS STRUCTURES
        1. 15.3.1. Agency Pass-Through RMBS
        2. 15.3.2. Agency Stripped MBS
          1. 15.3.2.1. Principal-Only Securities
          2. 15.3.2.2. Interest-Only Securities
        3. 15.3.3. Agency Collateralized Mortgage Obligations
          1. 15.3.3.1. Sequential-Pay Structures
          2. 15.3.3.2. Planned Amortization Class Bonds and Support Bonds
        4. 15.3.4. Private-Label RMBS
      4. 15.4. PRICING RMBS BY SIMULATION
        1. 15.4.1. Prepayment Models
          1. 15.4.1.1. Arctangent Model
          2. 15.4.1.2. Modified Goldman Sachs Model
        2. 15.4.2. Interest Rate Models
        3. 15.4.3. Putting It All Together
        4. 15.4.4. Further Analysis
          1. 15.4.4.1. Distribution of Path Values
          2. 15.4.4.2. Average Life
          3. 15.4.4.3. Option-Adjusted Spread
        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
        1. 15.5.1. Interest Rate Risk
        2. 15.5.2. Credit Risk
        3. 15.5.3. Model Risk
      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
          1. 16.1.1.1. Protective Put Strategies
          2. 16.1.1.2. Collar 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
          1. 16.2.1.1. Using Futures
          2. 16.2.1.2. Using Options
          3. 16.2.1.3. Using Swaps
        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
        1. 16.4.1. Approximate Portfolio Revaluation
        2. 16.4.2. Variance Reduction Techniques
      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
        1. 17.1.1. Classification According to Economic Life
        2. 17.1.2. Classification According to Risk
        3. 17.1.3. Classification According to Dependence on Other Projects
      2. 17.2. INVESTMENT DECISIONS AND WEALTH MAXIMIZATION
        1. 17.2.1. Cost of Capital, Required Rate of Return, and Discount Rate
        2. 17.2.2. Net Present Value
        3. 17.2.3. Profitability Index
        4. 17.2.4. Internal Rate of Return
        5. 17.2.5. Modified Internal Rate of Return
        6. 17.2.6. Payback Period and Discounted Payback Period
        7. 17.2.7. Issues in Capital Budgeting
          1. 17.2.7.1. Scale Differences
          2. 17.2.7.2. Unequal Lives
        8. 17.2.8. Capital Budgeting in Practice
      3. 17.3. EVALUATING PROJECT RISK
        1. 17.3.1. Measuring a Project's Market Risk
          1. 17.3.1.1. Computing the Cost of Capital Based on the CAPM
          2. 17.3.1.2. Adjusting the Company's Cost of Capital
        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
            1. 17.4.1.1.1. Revenues
            2. 17.4.1.1.2. Costs
          2. 17.4.1.2. Persistence
            1. 17.4.1.2.1. Revenues
            2. 17.4.1.2.2. Costs
        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
          1. 17.7.1.1. Creating the Simulation Inputs
          2. 17.7.1.2. Running the Simulation and Formatting Output
          3. 17.7.1.3. Creating Tornado Graphs
        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
        1. 18.6.1. Project to Abandon or Expand
        2. 18.6.2. Valuing an Option to Wait
        3. 18.6.3. Valuing a Multiperiod Real Estate Project
      7. 18.7. ESTIMATION OF INPUTS FOR REAL OPTION VALUATION MODELS
        1. 18.7.1. Discount Rate
        2. 18.7.2. Volatility
      8. 18.8. SUMMARY
      9. 18.9. SOFTWARE HINTS
      10. 18.10. NOTES
    3. References