Simulation and Optimization in Finance -- Contents -- Preface -- About the Authors -- Acknowledgments -- CHAPTER 1 Introduction -- OPTIMIZATION -- SIMULATION -- OUTLINE OF TOPICS -- PART One Fundamental Concepts -- CHAPTER 2 Important Finance Concepts -- 2.1 BASIC THEORY OF INTEREST -- 2.1.1 Compound Interest -- 2.1.2 Present Value and Future Value -- 2.2 ASSET CLASSES -- 2.2.1 Equities -- 2.2.2 Fixed Income Securities -- 2.3 BASIC TRADING TERMINOLOGY -- 2.3.1 Borrowing Funds to Purchase Securities -- 2.3.2 Long and Short Positions -- 2.4 CALCULATING RATE OF RETURN -- 2.5 VALUATION -- 2.5.1 Valuation Models for Equities -- 2.5.2 Valuation Models for Fixed Income Securities -- 2.6 IMPORTANT CONCEPTS IN FIXED INCOME -- 2.6.1 Spot Rates -- 2.6.2 The Term Structure -- 2.6.3 Forward Rates -- 2.6.4 Credit Spreads -- 2.6.5 Duration -- 2.6.6 Convexity -- 2.6.7 Key Rate Duration -- 2.6.8 Total Return -- SUMMARY -- NOTES -- CHAPTER 3 Random Variables, Probability Distributions, and Important Statistical Concepts -- 3.1 WHAT IS A PROBABILITY DISTRIBUTION? -- 3.2 BERNOULLI PROBABILITY DISTRIBUTION AND PROBABILITY MASS FUNCTIONS -- 3.3 BINOMIAL PROBABILITY DISTRIBUTION AND DISCRETE DISTRIBUTIONS -- 3.4 NORMAL DISTRIBUTION AND PROBABILITY DENSITY FUNCTIONS -- 3.5 CONCEPT OF CUMULATIVE PROBABILITY -- 3.6 DESCRIBING DISTRIBUTIONS -- 3.6.1 Measures of Central Tendency -- 3.6.2 Measures of Risk -- 3.6.3 Skew -- 3.6.4 Kurtosis -- 3.7 BRIEF OVERVIEW OF SOME IMPORTANT PROBABILITY DISTRIBUTIONS -- 3.7.1 Discrete Distributions -- 3.7.2 Continuous Distributions -- 3.8 DEPENDENCE BETWEEN TWO RANDOM VARIABLES: COVARIANCE AND CORRELATION -- 3.9 SUMS OF RANDOM VARIABLES -- 3.10 JOINT PROBABILITY DISTRIBUTIONS AND CONDITIONAL PROBABILITY -- 3.11 FROM PROBABILITY THEORY TO STATISTICAL MEASUREMENT: PROBABILITY DISTRIBUTIONS AND SAMPLING -- 3.11.1 Central Limit Theorem.

3.11.2 Confidence Intervals -- 3.11.3 Bootstrapping -- 3.11.4 Hypothesis Testing -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 4 Simulation Modeling -- 4.1 MONTE CARLO SIMULATION: A SIMPLE EXAMPLE -- 4.1.1 Selecting Probability Distributions for the Inputs -- 4.1.2 Interpreting Monte Carlo Simulation Output -- 4.2 WHY USE SIMULATION? -- 4.2.1 Multiple Input Variables and Compounding Distributions -- 4.2.2 Incorporating Correlations -- 4.2.3 Evaluating Decisions -- 4.3 IMPORTANT QUESTIONS IN SIMULATION MODELING -- 4.3.1 How Many Scenarios? -- 4.3.2 Estimator Bias -- 4.3.3 Estimator Efficiency -- 4.4 RANDOM NUMBER GENERATION -- 4.4.1 Inverse Transform Method -- 4.4.2 What Defines a "Good" Random Number Generator? -- 4.4.3 Pseudorandom Number Generators -- 4.4.4 Quasirandom (Low-Discrepancy) Sequences -- 4.4.5 Stratified Sampling -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 5 Optimization Modeling -- 5.1 OPTIMIZATION FORMULATIONS -- 5.1.1 Minimization vs. Maximization -- 5.1.2 Local vs. Global Optima -- 5.1.3 Multiple Objectives -- 5.2 IMPORTANT TYPES OF OPTIMIZATION PROBLEMS -- 5.2.1 Convex Programming -- 5.2.2 Linear Programming -- 5.2.3 Quadratic Programming -- 5.2.4 Second-Order Cone Programming -- 5.2.5 Integer and Mixed Integer Programming -- 5.3 OPTIMIZATION PROBLEM FORMULATION EXAMPLES -- 5.3.1 Portfolio Allocation -- 5.3.2 Cash Flow Matching -- 5.3.3 Capital Budgeting -- 5.4 OPTIMIZATION ALGORITHMS -- 5.4.1 Linear Optimization: The Simplex Algorithm and Interior Point Methods -- 5.4.2 Constrained Nonlinear Optimization: The KKT Conditions and Lagrange Multipliers -- 5.4.3 Integer Programming Algorithms -- 5.4.4 Randomized Search Algorithms -- 5.4.5 Algorithm Efficiency -- 5.5 OPTIMIZATION DUALITY -- 5.6 MULTISTAGE OPTIMIZATION -- 5.6.1 Finite State Space -- 5.6.2 Infinite State Space.

5.6.3 Steps in Formulating Multistage Optimization Problems -- 5.7 OPTIMIZATION SOFTWARE -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 6 Optimization under Uncertainty -- 6.1 DYNAMIC PROGRAMMING -- 6.2 STOCHASTIC PROGRAMMING -- 6.2.1 Multistage Models -- 6.2.2 Mean-Risk Stochastic Models -- 6.2.3 Chance-Constrained Models -- 6.3 ROBUST OPTIMIZATION -- 6.3.1 Uncertainty Sets and Robust Counterparts -- 6.3.2 Multistage Robust Optimization -- SUMMARY -- NOTES -- PART Two Portfolio Optimization and Risk Measures -- CHAPTER 7 Asset Diversification and Efficient Frontiers -- 7.1 THE CASE FOR DIVERSIFICATION -- 7.2 THE CLASSICAL MEAN-VARIANCE OPTIMIZATION FRAMEWORK -- 7.3 EFFICIENT FRONTIERS -- 7.4 ALTERNATIVE FORMULATIONS OF THE CLASSICAL MEAN-VARIANCE OPTIMIZATION PROBLEM -- 7.4.1 Expected Return Formulation -- 7.4.2 Risk Aversion Formulation -- 7.5 THE CAPITAL MARKET LINE -- 7.6 EXPECTED UTILITY THEORY -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 8 Advances in the Theory of Portfolio Risk Measures -- 8.1 CLASSES OF RISK MEASURES -- 8.1.1 Dispersion Risk Measures -- 8.1.2 Downside Risk Measures -- 8.2 VALUE-AT-RISK -- 8.2.1 The History of the Value-at-Risk Metric -- 8.2.2 Calculation of Value-at-Risk for a Normal Distribution -- 8.2.3 Calculation of Value-at-Risk Using Historical and Simulated Data Scenarios -- 8.2.4 VaR Calculation Example -- 8.2.5 Selection of Value-at-Risk Parameters and Regulatory Requirements -- 8.2.6 Optimization of Value-at-Risk -- 8.2.7 Arguments For and Against Value-at-Risk -- 8.3 CONDITIONAL VALUE-AT-RISK AND THE CONCEPT OF COHERENT RISK MEASURES -- 8.3.1 Estimation of Conditional Value-at-Risk from a Normal Distribution -- 8.3.2 Estimation of Conditional Value-at-Risk from a Discrete Distribution -- 8.3.3 Optimization of Conditional Value-at-Risk -- SUMMARY -- SOFTWARE HINTS -- NOTES.

CHAPTER 9 Equity Portfolio Selection in Practice -- 9.1 THE INVESTMENT PROCESS -- 9.1.1 Setting Investment Objectives -- 9.1.2 Developing and Implementing a Portfolio Strategy -- 9.1.3 Monitoring the Portfolio -- 9.1.4 Adjusting the Portfolio -- 9.2 PORTFOLIO CONSTRAINTS COMMONLY USED IN PRACTICE -- 9.2.1 Long-Only (No-Short-Selling) Constraints -- 9.2.2 Holding Constraints -- 9.2.3 Turnover Constraints -- 9.2.4 Risk Factor Constraints -- 9.2.5 Cardinality Constraints -- 9.2.6 Minimum Holding and Transaction Size Constraints -- 9.2.7 Round Lot Constraints -- 9.3 BENCHMARK EXPOSURE AND TRACKING ERROR MINIMIZATION -- 9.3.1 Standard Definition of Tracking Error -- 9.3.2 Alternative Ways of Defining Tracking Error -- 9.3.3 Actual vs. Predicted Tracking Error -- 9.4 INCORPORATING TRANSACTION COSTS -- 9.4.1 Linear Transaction Costs -- 9.4.2 Piecewise-Linear Transaction Costs -- 9.4.3 Quadratic Transaction Costs -- 9.4.4 Fixed Transaction Costs -- 9.5 INCORPORATING TAXES -- 9.6 MULTIACCOUNT OPTIMIZATION -- 9.7 ROBUST PARAMETER ESTIMATION -- 9.8 PORTFOLIO RESAMPLING -- 9.9 ROBUST PORTFOLIO OPTIMIZATION -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 10 Fixed Income Portfolio Management in Practice -- 10.1 MEASURING BOND PORTFOLIO RISK -- 10.1.1 Interest Rate Risk -- 10.1.2 Yield Curve Risk -- 10.1.3 Spread Risk -- 10.1.4 Credit Risk -- 10.1.5 Estimating Value-at-Risk for Fixed Income Securities -- 10.2 THE SPECTRUM OF BOND PORTFOLIO MANAGEMENT STRATEGIES -- 10.2.1 Bond Market Indices -- 10.2.2 Pure Bond Indexing Strategy -- 10.2.3 Enhanced Indexing/Matching Primary Risk Factors Approach -- 10.2.4 Enhanced Indexing/Minor Risk Factor Mismatches -- 10.2.5 Active Management/Larger Risk Factor Mismatches -- 10.2.6 Active Management/Full-Blown Active -- 10.2.7 Using Quantitative Methods for Portfolio Allocation -- 10.3 LIABILITY-DRIVEN STRATEGIES.

10.3.1 Immunization Strategy for a Single-Period Liability -- 10.3.2 Cash Flow Matching Strategy -- SUMMARY -- NOTES -- PART Three Asset Pricing Models -- CHAPTER 11 Factor Models -- 11.1 THE CAPITAL ASSET PRICING MODEL -- 11.2 THE ARBITRAGE PRICING THEORY -- 11.3 BUILDING MULTIFACTOR MODELS IN PRACTICE -- 11.3.1 Regression Analysis -- 11.3.2 Factor Analysis -- 11.3.3 Principal Components Analysis -- 11.4 APPLICATIONS OF FACTOR MODELS IN PORTFOLIO MANAGEMENT -- 11.4.1 Portfolio Performance Measurement -- 11.4.2 Risk Decomposition in Equity Portfolios -- 11.4.3 Efficient Mean-Variance Optimization -- 11.4.4 Risk Decomposition in Bond Portfolios -- SUMMARY -- SOFTWARE HINTS -- NOTES -- CHAPTER 12 Modeling Asset Price Dynamics -- 12.1 BINOMIAL TREES -- 12.2 ARITHMETIC RANDOM WALKS -- 12.2.1 Simulation -- 12.2.2 Parameter Estimation -- 12.2.3 Arithmetic Random Walk: Some Additional Facts -- 12.3 GEOMETRIC RANDOM WALKS -- 12.3.1 Simulation -- 12.3.2 Parameter Estimation -- 12.3.3 Geometric Random Walk: Some Additional Facts -- 12.4 MEAN REVERSION -- 12.4.1 Simulation -- 12.4.2 Parameter Estimation -- 12.4.3 The Cox-Ingersoll-Ross Model for Interest Rates Dynamics -- 12.4.4 Geometric Mean Reversion -- 12.5 ADVANCED RANDOM WALK MODELS -- 12.5.1 Correlated Random Walks -- 12.5.2 Incorporating Jumps -- 12.5.3 Stochastic Volatility -- 12.6 STOCHASTIC PROCESSES -- SUMMARY -- SOFTWARE HINTS -- NOTES -- PART Four Derivative Pricing and Use -- CHAPTER 13 Introduction to Derivatives -- 13.1 BASIC TYPES OF DERIVATIVES -- 13.1.1 Forwards and Futures -- 13.1.2 Options -- 13.1.3 Swaps -- 13.2 IMPORTANT CONCEPTS FOR DERIVATIVE PRICING AND USE -- 13.2.1 Arbitrage -- 13.2.2 Hedging -- 13.3 PRICING FORWARDS AND FUTURES -- 13.4 PRICING OPTIONS -- 13.4.1 Using Binomial Trees to Price European Options -- 13.4.2 The Black-Scholes Formula for European Options.

13.4.3 Pricing American Options with Binomial Trees.