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Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Book Description

Volume III Valuation, Financial Modeling, and Quantitative Tools contains the most comprehensive coverage of the analytical tools, risk measurement methods, and valuation techniques currently used in the field of finance. It details a variety of concepts, such as credit risk modeling, Black-Scholes option pricing, and Monte Carlo simulation, and offers practical insights on effectively applying them to real-world situations.

Incorporating timely research and in-depth analysis, the Handbook of Finance is a comprehensive 3-Volume Set that covers both established and cutting-edge theories and developments in finance and investing. Other volumes in the set: Handbook of Finance Volume I: Financial Markets and Instruments and Handbook of Finance Volume II: Investment Management and Financial Management."

Table of Contents

  1. Copyright
  2. About the Editor
  3. Contributors
  4. Preface
  5. Guide to the Handbook of Finance
  6. 1. Risk Management
    1. 1. Risk and the French Connection
      1. 1.1. BLAISE PASCAL, THE NEUROTIC GENIUS
      2. 1.2. GAMBLING INTO MATHEMATICS
      3. 1.3. THE MAGIC OF THE MAGIC TRIANGLE
      4. 1.4. THE MORAL AND THE MORALS OF THE STORY
      5. 1.5. PASCAL'S WAGER
      6. 1.6. THE ART OF THINKING
      7. 1.7. SUMMARY
    2. REFERENCES
    3. 2. Risk: Traditional Finance versus Behavioral Finance
      1. 2.1. WHAT IS RISK?
      2. 2.2. THE DIFFERENT MEANINGS OF RISK
      3. 2.3. WHAT IS THE DIFFERENCE BETWEEN RISK AND UNCERTAINTY?
      4. 2.4. THE FINANCIAL PERSPECTIVE OF RISK FROM TWO SCHOOLS OF ACADEMIC THOUGHT
      5. 2.5. WHAT IS TRADITIONAL FINANCE?
        1. 2.5.1. The Basic Concepts of the Traditional Finance Perspective of Risk
        2. 2.5.2. Modern Portfolio Theory
        3. 2.5.3. Measures of Dispersion: Standard Deviation/Variance versus Semivariance
        4. 2.5.4. The Capital Asset Pricing Model
        5. 2.5.5. The "Great Beta Debate" in Academic Finance
        6. 2.5.6. The Basic Viewpoint of Traditional Finance Researchers: The Objective (Quantitative) Nature of Risk
      6. 2.6. WHAT IS BEHA VIORAL FINANCE?
        1. 2.6.1. The Behavioral Finance Viewpoint of Risk
        2. 2.6.2. The Basic Viewpoint of Behavioral Finance Researchers: The Subjective (Qualitative) Nature of Risk
        3. 2.6.3. The Behavioral Finance Perspective: The Inverse (Negative) Relationship between Perceived Risk and Return
      7. 2.7. SUMMARY
      8. 2.8. ACKNOWLEDGMENTS
    4. REFERENCES
    5. 3. Overview of Risk Management and Alternative Risk Transfer
      1. 3.1. RISK AND RETURN
      2. 3.2. ACTIVE RISK MANAGEMENT
        1. 3.2.1. Risk Management Processes
        2. 3.2.2. Risk Management Techniques
        3. 3.2.3. General Risk Management Considerations
      3. 3.3. RISK CONCEPTS
        1. 3.3.1. Expected Value and Variance
        2. 3.3.2. Risk Aversion
        3. 3.3.3. Risk Transfer and the Insurance Mechanism
        4. 3.3.4. Diversification and Risk Pooling
        5. 3.3.5. Hedging
        6. 3.3.6. Moral Hazard, Adverse Selection, and Basis Risk
        7. 3.3.7. Noninsurance Transfers
      4. 3.4. OVERVIEW OF ART
        1. 3.4.1. ART Background and Trends
        2. 3.4.2. Product and Market Convergence
    6. REFERENCES
    7. 4. Risk and Risk Management
      1. 4.1. FINANCIAL VERSUS NONFINANCIAL RISKS
        1. 4.1.1. Financial Risks
          1. 4.1.1.1. Market Risk
          2. 4.1.1.2. Funding Risk
          3. 4.1.1.3. Market Liquidity Risk
          4. 4.1.1.4. Credit Risk
          5. 4.1.1.5. Legal Risk
        2. 4.1.2. Perils, Accidents, and Hazards
          1. 4.1.2.1. Production Perils and Business Continuity Risks
          2. 4.1.2.2. Operational Perils
      2. 4.2. CORE VERSUS NONCORE RISKS
      3. 4.3. RISK MANAGEMENT ALTERNATIVES
        1. 4.3.1. Risk Retention and Risk Finance
          1. 4.3.1.1. Funded and Unfunded Retentions
          2. 4.3.1.2. Preloss versus Postloss Funding
        2. 4.3.2. Risk Neutralization
          1. 4.3.2.1. Risk Reduction, Prevention, and Control
          2. 4.3.2.2. Risk Consolidation
        3. 4.3.3. Risk Transfer
          1. 4.3.3.1. Counterparties to Risk Transfer Agreements
          2. 4.3.3.2. Types of Risk Transfer
          3. 4.3.3.3. Limitation of Liability
          4. 4.3.3.4. Funded versus Unfunded Risk Transfer Solutions
      4. 4.4. SUMMARY
    8. REFERENCES
    9. 5. Risk Management for Asset Management Firms
      1. 5.1. IMPORTANCE OF CLIENT RISK REPORTING
      2. 5.2. RISK MANAGEMENT IN DETAIL
        1. 5.2.1. Value at Risk
          1. 5.2.1.1. Style VaR and Cornish-Fisher
          2. 5.2.1.2. Incremental VaR
          3. 5.2.1.3. Beyond VaR
        2. 5.2.2. Factor Models and Risk Management
          1. 5.2.2.1. Explicit Factor Models
          2. 5.2.2.2. Implicit Factor Models
          3. 5.2.2.3. Hybrid or Multi-Index Model
        3. 5.2.3. Growing Importance of the Compliance Function
        4. 5.2.4. Credit Risk Approaches
          1. 5.2.4.1. Merton Model
          2. 5.2.4.2. Reduced-Form Model
      3. 5.3. SUMMARY
    10. REFERENCES
    11. 6. Catastrophe and Risk
      1. 6.1. NATURE OF CATASTROPHE
        1. 6.1.1. Definition
        2. 6.1.2. Frequency
        3. 6.1.3. Vulnerability
        4. 6.1.4. Measuring Severity
      2. 6.2. SCOPE OF IMPACT
      3. 6.3. CATASTROPHE AND THE RISK MANAGEMENT FRAMEWORK
      4. 6.4. SUMMARY
    12. REFERENCES
    13. 7. Overview of Enterprise Risk Management
      1. 7.1. THE BENEFITS OF ERM
      2. 7.2. THE CHIEF RISK OFFICER
        1. 7.2.1. The Role of the CRO
        2. 7.2.2. The Ideal CRO
      3. 7.3. COMPONENTS OF ERM
        1. 7.3.1. Corporate Governance
        2. 7.3.2. Line Management
        3. 7.3.3. Portfolio Management
        4. 7.3.4. Risk Transfer
        5. 7.3.5. Risk Analytics
        6. 7.3.6. Data and Technology Resources
        7. 7.3.7. Stakeholder Management
      4. 7.4. SUMMARY
    14. REFERENCES
    15. 8. Model Risk
      1. 8.1. MODELS AND MODEL RISK
      2. 8.2. SOURCES OF MODEL RISK
        1. 8.2.1. Incorrect Model Specification
        2. 8.2.2. Incorrect Model Application
        3. 8.2.3. Implementation Risk
        4. 8.2.4. Endogenous Model Risk
        5. 8.2.5. Other Sources of Model Risk
      3. 8.3. MANAGING MODEL RISK
        1. 8.3.1. Some Guidelines for Risk Managers
        2. 8.3.2. Some Institutional Guidelines
      4. 8.4. SUMMARY
    16. REFERENCES
    17. 9. Back-Testing Market Risk Models
      1. 9.1. STATISTICAL BACK-TESTING
      2. 9.2. EXCEEDANCE-BASED STATISTICAL APPROACHES
        1. 9.2.1. Binomial (Kupiec) Approach
        2. 9.2.2. A Normal Approximation
        3. 9.2.3. Tests of Independence
        4. 9.2.4. Conditional Testing (Christoffersen) Approach
        5. 9.2.5. Strengths and Limitations of Exceedance-Based Approaches
      3. 9.3. STATISTICAL BACK-TESTING OF VaRs AT MULTIPLE CONFIDENCE LEVELS
        1. 9.3.1. Testing Uniformity
        2. 9.3.2. Applying the Berkowitz Transformation and Testing for Standard Normality
        3. 9.3.3. Tests Applied to Truncated Distributions
      4. 9.4. USING BACK-TESTS FOR DIAGNOSTIC PURPOSES
      5. 9.5. RANKING ALTERNATIVE MODELS
      6. 9.6. SUMMARY
    18. REFERENCES
    19. 10. Risk Measures and Portfolio Selection
      1. 10.1. DESIRABLE FEATURES OF INVESTMENT RISK MEASURES
        1. 10.1.1. Basic Features of Investment Risk Measures
        2. 10.1.2. Intertemporal Dependence and Correlation with Other Sources of Risk
      2. 10.2. ALTERNATIVE RISK MEASURES FOR PORTFOLIO SELECTION
      3. 10.3. DISPERSION MEASURES
        1. 10.3.1. Mean Standard Deviation
        2. 10.3.2. Mean Absolute Deviation
        3. 10.3.3. Mean Absolute Moment
        4. 10.3.4. Gini Index of Dissimilarity
        5. 10.3.5. Mean Entropy
        6. 10.3.6. Mean Colog
      4. 10.4. SAFETY-FIRST RISK MEASURES
        1. 10.4.1. Classical Safety First
        2. 10.4.2. Value at Risk
        3. 10.4.3. Conditional Value at Risk/Expected Tail Loss
        4. 10.4.4. MiniMax
        5. 10.4.5. Lower Partial Moment
        6. 10.4.6. Power Conditional Value at Risk
      5. 10.5. SUMMARY
    20. REFERENCES
    21. 11. Statistical Models of Operational Loss
      1. 11.1. OPERATIONAL RISKS
        1. 11.1.1. Definitions of Operational Risks
        2. 11.1.2. Frequency and Severity
        3. 11.1.3. Probability-Impact Diagrams
        4. 11.1.4. Data Considerations
          1. 11.1.4.1. Scorecards
          2. 11.1.4.2. External Data
      2. 11.2. BAYESIAN ESTIMATION
        1. 11.2.1. Bayesian Estimation of Loss Severity Parameters
          1. 11.2.1.1. Estimating the Mean and Standard Deviation of a Loss Severity Distribution
          2. 11.2.1.2. Bayesian Estimation of Loss Probability
          3. 11.2.1.3. Estimating the Loss Probability Using Internal Data Combined with (a) External Data and (b) Scorecard Data
      3. 11.3. INTRODUCING THE ADVANCED MEASUREMENT APPROACHES
        1. 11.3.1. A General Framework for the Advanced Measurement Approach
        2. 11.3.2. Functional Forms for Loss Frequency and Severity Distributions
        3. 11.3.3. Comments on Parameter Estimation
        4. 11.3.4. Comments on the 99.9th Percentile
      4. 11.4. ANALYTIC APPROXIMATIONS TO UNEXPECTED ANNUAL LOSS
        1. 11.4.1. A Basic Formula for the ORR
        2. 11.4.2. Calibration: Normal, Poisson, and Negative Binomial Frequencies
          1. 11.4.2.1. ORR for Two Risk Types
        3. 11.4.3. The ORR with Random Severity
          1. 11.4.3.1. Comparison of Bayesian and Classical Estimates of ORR
        4. 11.4.4. Inclusion of Insurance and the General Formula
      5. 11.5. SIMULATING THE ANNUAL LOSS DISTRIBUTION
        1. 11.5.1. Comparison of ORR from Analytic and Simulation Approximations
      6. 11.6. AGGREGATION AND THE TOTAL LOSS DISTRIBUTION
        1. 11.6.1. Aggregation of Analytic Approximations to the ORR
        2. 11.6.2. Comments on Correlation and Dependency
        3. 11.6.3. The Aggregation Algorithm
        4. 11.6.4. Aggregation of Annual Loss Distributions under Different Dependency Assumptions
        5. 11.6.5. Specifying Dependencies
      7. 11.7. SUMMARY
    22. REFERENCES
    23. 12. Risk Management in Freight Markets with Forwards and Options Contracts
      1. 12.1. FREIGHT FORWARD AGREEMENTS
        1. 12.1.1. FFA Contract Specification
        2. 12.1.2. Freight Options Market
      2. 12.2. FREIGHT RATE DYNAMICS
        1. 12.2.1. Freight Market Equilibrium Theory
        2. 12.2.2. Modeling Forward Freight Rate Dynamics
      3. 12.3. MODELING OF FREIGHT RATE DERIVATIVES
        1. 12.3.1. Theoretical Framework
        2. 12.3.2. Deriving FFA from Spot Price
        3. 12.3.3. Freight Rate Options
        4. 12.3.4. Spot Freight Rate Dynamics
        5. 12.3.5. The Black Model for Freight Rate Options
        6. 12.3.6. Lognormal Approximation for FFA Dynamics when t < T1
        7. 12.3.7. Exemplifications
      4. 12.4. MONTE CARLO SIMULATION
        1. 12.4.1. Option Pricing
        2. 12.4.2. Empirical Results
      5. 12.5. SUMMARY
    24. REFERENCES
    25. 13. Fixed Income Risk Modeling
      1. 13.1. MODELING FRAMEWORK
      2. 13.2. INTEREST RATE RISK
      3. 13.3. SPREAD RISK—THE CONVENTIONAL APPROACH
        1. 13.3.1. Swap Spread Factors
      4. 13.4. DETAILED CREDIT SPREAD FACTORS
        1. 13.4.1. Emerging Markets Spread Factors
      5. 13.5. EMPIRICAL CREDIT RISK
      6. 13.6. IMPLIED PREPAYMENT RISK
      7. 13.7. IMPLIED VOLATILITY RISK
      8. 13.8. SPECIFIC RISK
      9. 13.9. CURRENCY RISK
      10. 13.10. GLOBAL MODEL INTEGRATION
        1. 13.10.1. Coping with Incomplete Return Series
        2. 13.10.2. Global Integration
      11. 13.11. THE MODEL IN ACTION
      12. 13.12. SUMMARY
    26. REFERENCES
    27. 14. Effective Duration and Convexity
      1. 14.1. EFFECTIVE DURATION AND EFFECTIVE CONVEXITY—AN EXAMPLE
        1. 14.1.1. Straight Bond
        2. 14.1.2. Callable Bond
        3. 14.1.3. Putable Bond
      2. 14.2. PUTTING IT ALL TOGETHER
      3. 14.3. SUMMARY
    28. REFERENCES
    29. 15. Duration Estimation for Bonds and Bond Portfolios
      1. 15.1. DURATION
      2. 15.2. DOLLAR DURATION
      3. 15.3. MODIFIED DURATION, MACAULAY DURATION, AND EFFECTIVE DURATION
      4. 15.4. SPREAD DURATION FOR FIXED-RATE BONDS
      5. 15.5. DURATION OF A FLOATING-RATE SECURITY
      6. 15.6. PORTFOLIO DURATION
        1. 15.6.1. Contribution to Portfolio Duration
      7. 15.7. SUMMARY
    30. REFERENCES
    31. 16. Yield Curve Risk Measures
      1. 16.1. DURATION, CONVEXITY, AND NONPARALLEL YIELD CURVE SHIFTS
      2. 16.2. CASH-FLOW DISTRIBUTION ANALYSIS VERSUS A BENCHMARK
      3. 16.3. KEY RATE DURATION
      4. 16.4. SLOPE ELASTICITY MEASURE
      5. 16.5. YIELD CURVE RESHAPING DURATION
      6. 16.6. ANALYSIS OF LIKELY YIELD CURVE SHIFTS
      7. 16.7. SUMMARY
    32. REFERENCES
    33. 17. Improving Guidelines for Interest Rate and Credit Derivatives
      1. 17.1. FUTURES AND FORWARD CONTRACTS
      2. 17.2. DURATION AND FUTURES POSITIONS
      3. 17.3. GUIDELINES FOR INTEREST RATE FUTURES
      4. 17.4. WHAT ABOUT LEVERAGE?
      5. 17.5. APPLICATION TO OTHER INTEREST RATE DERIVATIVE INSTRUMENTS
      6. 17.6. CREDIT DEFAULT SWAP GUIDELINES
      7. 17.7. LOAN GUIDELINES
      8. 17.8. SUMMARY
    34. REFERENCES
    35. 18. Modeling Portfolio Credit Risk
      1. 18.1. QUANTIFYING PORTFOLIO CREDIT RISK
        1. 18.1.1. Key Observations
      2. 18.2. CREDIT RISK UNDER DEFAULT MODE
        1. 18.2.1. Default Correlation
        2. 18.2.2. Relationship to Loss Correlation
        3. 18.2.3. Estimating Default Correlation
        4. 18.2.4. Key Observations
      3. 18.3. ESTIMATING ASSET RETURN CORRELATION
        1. 18.3.1. Remarks
        2. 18.3.2. Factor Models
        3. 18.3.3. Approximate Asset Return Correlations
      4. 18.4. CREDIT RISK UNDER MIGRATION MODE
        1. 18.4.1. Computing Joint Migration Probabilities
        2. 18.4.2. Computing Joint Credit Loss
        3. 18.4.3. Portfolio Credit Risk
      5. 18.5. SUMMARY
    36. REFERENCES
    37. 19. The Basics of Cash-Market Hedging
      1. 19.1. THE MECHANICS OF HEDGING
        1. 19.1.1. Identifying the Sources of Price Risk
        2. 19.1.2. Balancing Risk and Return
        3. 19.1.3. Choosing a Hedge Instrument
        4. 19.1.4. Determining the Appropriate Hedge Position Using DVBP
        5. 19.1.5. The Hedge Ratio
        6. 19.1.6. Adjusted Hedge Ratio
        7. 19.1.7. 10-Year Treasury-Note Equivalent
      2. 19.2. HEDGING A NONCALLABLE BOND
        1. 19.2.1. Yield-Spread Risk
        2. 19.2.2. Cost of Carry
          1. 19.2.2.1. Long Carry
        3. 19.2.3. Short Carry
        4. 19.2.4. Net Carry
          1. 19.2.4.1. Negative Carry: A Treasury "Goes on Special"
        5. 19.2.5. Incorporating Carry into a Hedge
      3. 19.3. HEDGING SECURITIES WITH OFF-THE-RUN MATURITIES
      4. 19.4. HEDGING OPTION-EMBEDDED BONDS
        1. 19.4.1. Option-Embedded Corporate Bonds
        2. 19.4.2. Mortgage Pass-Through Securities
      5. 19.5. Hedging Considerations for Option-Embedded Notes
      6. 19.6. SUMMARY
    38. REFERENCES
    39. 20. Hedging Fixed Income Securities with Interest Rate Swaps
      1. 20.1. CHARACTERIZING INTEREST RATE SWAPS
        1. 20.1.1. Swaps as Financed Bond Positions
      2. 20.2. PRICING OF INTEREST RATE SWAPS
        1. 20.2.1. Interest Rate Sensitivity of a Swap
        2. 20.2.2. DVBP of a Swap
        3. 20.2.3. Hedging with Interest Rate Swaps
        4. 20.2.4. Hedge Ratio
        5. 20.2.5. Corporate Bond Hedge
        6. 20.2.6. Mortgage-Backed Security Hedge
        7. 20.2.7. Swaps versus Other Hedge Instruments
      3. 20.3. SUMMARY
    40. REFERENCES
    41. 21. Yield Curve Risk Management
      1. 21.1. SINGLE-FACTOR YIELD CURVE MODELS
        1. 21.1.1. Mathematical Framework
        2. 21.1.2. Yield-to-Maturity Approach
        3. 21.1.3. Other Single-Factor Models
        4. 21.1.4. Single-Factor Yield Curve Management
        5. 21.1.5. Single (and Multi)Factor Yield Curve Management Failure
        6. 21.1.6. Single-Factor Yield Curve Management: The Time Dynamic
        7. 21.1.7. Is There a "Best" Single-Factor Model?
      2. 21.2. MULTIFACTOR YIELD CURVE MODELS
        1. 21.2.1. Mathematical Framework
        2. 21.2.2. Multifactor Models
        3. 21.2.3. Relationships Between Single- and Multifactor Models
        4. 21.2.4. Is There a "Best" Multifactor Model?
        5. 21.2.5. Multifactor Yield Curve Management I
        6. 21.2.6. Multifactor Yield Curve Management II
        7. 21.2.7. Additional Considerations for Multifactor Models
      3. 21.3. SUMMARY
    42. REFERENCES
  7. 2. Interest Rate Modeling
    1. 22. The Concept and Measures of Interest Rate Volatility
      1. 22.1. BASIC DEFINITIONS AND FIRST FINDINGS
      2. 22.2. A DIFFUSIVE MODEL FOR RANDOMNESS
        1. 22.2.1. A Brief Excursion to Brownian Motion
      3. 22.3. MEAN REVERSION AND MARKET STABILITY
      4. 22.4. THE RATE DISTRIBUTION
      5. 22.5. INTEREST RATE JUMPS
      6. 22.6. SUMMARY
      7. 22.7. ACKNOWLEDGMENTS
    2. REFERENCES
    3. 23. Short-Rate Term Structure Models
      1. 23.1. THE CONCEPT OF SHORT-RATE MODELING
        1. 23.1.1. The Arbitrage-Free Inter-Rate Relationship
        2. 23.1.2. Consistency with the Initial Yield Curve
        3. 23.1.3. Consistency with European Option Values
      2. 23.2. SINGLE-FACTOR SHORT-RATE MODELS
        1. 23.2.1. The Hull-White Model
        2. 23.2.2. The Cox-Ingersoll-Ross Model
        3. 23.2.3. The Squared Gaussian (SqG) Model (also known as Quadratic Model)
        4. 23.2.4. The Black-Karasinski Model
        5. 23.2.5. The Flesaker-Hughston Model
        6. 23.2.6. Other Single-Factor Models
        7. 23.2.7. Calibration Issues
      3. 23.3. WHICH MODEL IS BETTER?
        1. 23.3.1. Measuring Volatility Skew
        2. 23.3.2. Using Volatility Index
      4. 23.4. ADDING A SECOND FACTOR TO SHORT-RATE MODELS
      5. 23.5. THE CONCEPT OF AFFINE MODELING
        1. 23.5.1. The Jump-Diffusion Case
      6. 23.6. SUMMARY
      7. 23.7. ACKNOWLEDGMENTS
    4. REFERENCES
  8. 3. Credit Risk Modeling and Analysis
    1. 24. Credit Risk
      1. 24.1. CREDIT DEFAULT RISK
        1. 24.1.1. Credit Ratings
        2. 24.1.2. Factors Considered in Rating Corporate Bond Issues
        3. 24.1.3. Factors Considered in Rating Sovereign Debt
        4. 24.1.4. Bankruptcy and Creditor Rights in the United States
          1. 24.1.4.1. The Bankruptcy Process
          2. 24.1.4.2. Absolute Priority: Theory and Practice
        5. 24.1.5. Default and Recovery Rates
        6. 24.1.6. Counterparty Risk
      2. 24.2. CREDIT SPREAD RISK
        1. 24.2.1. Fundamental Factors that Affect Credit Spreads
          1. 24.2.1.1. Macro Fundamentals
          2. 24.2.1.2. Micro Fundamentals
      3. 24.3. DOWNGRADE RISK
        1. 24.3.1. Rating Migration (Transition) Table
      4. 24.4. CREDIT RISK TRANSFER MECHANISMS
      5. 24.5. SUMMARY
    2. REFERENCES
    3. 25. Credit Risk Modeling Using Structural Models
      1. 25.1. COMPLEXITIES IN CREDIT RISK MODELING
      2. 25.2. OVERVIEW OF CURRENT MODELS
      3. 25.3. THE BLACK-SCHOLES-MERTON MODEL
        1. 25.3.1. Implications of BSM Model
      4. 25.4. GESKE COMPOUND OPTION MODEL
      5. 25.5. BARRIER STRUCTURAL MODELS
      6. 25.6. ADVANTAGES AND DRAWBACKS OF STRUCTURAL MODELS
      7. 25.7. SUMMARY
    4. REFERENCES
    5. 26. Credit Risk Modeling Using Reduced-Form Models
      1. 26.1. THE POISSON PROCESS
      2. 26.2. THE JARROW-TURNBULL MODEL
      3. 26.3. THE CALIBRATION OF JARROW-TURNBULL MODEL
        1. 26.3.1. Transition Matrix
      4. 26.4. THE DUFFIE-SINGLETON MODEL
      5. 26.5. GENERAL OBSERVATIONS ON REDUCED-FORM MODELS
      6. 26.6. OTHER MODELS
        1. 26.6.1. Spread-Based Models
        2. 26.6.2. Hazard Models
      7. 26.7. SUMMARY
    6. REFERENCES
    7. 27. The Credit Analysis of Municipal Bonds
      1. 27.1. GENERAL OBLIGATION BONDS
        1. 27.1.1. Debt Burden
        2. 27.1.2. Budgetary Soundness
        3. 27.1.3. Tax Burden
        4. 27.1.4. Overall Economy
      2. 27.2. RED FLAGS FOR THE GENERAL OBLIGATION BOND ANALYST
      3. 27.3. REVENUE BONDS
        1. 27.3.1. Limits of the Basic Security
        2. 27.3.2. Flow-of-Funds Structure
        3. 27.3.3. Rate, User Charge, or Dedicated Revenue and Tax Covenants
        4. 27.3.4. The Priority of Pledged Revenue Claims
        5. 27.3.5. Additional-Bonds Test
        6. 27.3.6. Other Relevant Covenants and Issues
      4. 27.4. ANALYSIS BY TYPE OF REVENUE BOND
        1. 27.4.1. Airport Bonds
        2. 27.4.2. Hospital Bonds
        3. 27.4.3. Public Power Bonds
        4. 27.4.4. Highway and Bridge Bonds
        5. 27.4.5. Water and Sewer Bonds
      5. 27.5. RED FLAGS FOR THE REVENUE BOND ANALYST
      6. 27.6. SPECIAL SECURITY STRUCTURES
        1. 27.6.1. Refunded Bonds
          1. 27.6.1.1. Pure versus Mixed Escrow Funds
          2. 27.6.1.2. Two Major Types of Refunded Bonds
          3. 27.6.1.3. Determining the Safety of the Refunded Bonds
        2. 27.6.2. Tax and Bond Anticipation Notes
          1. 27.6.2.1. Reasons for Issuance
          2. 27.6.2.2. Security behind Tax and Revenue Anticipation Notes
          3. 27.6.2.3. Information Needed before Buying Tax or Revenue Anticipation Notes
        3. 27.6.3. Lease-Rental Bonds
        4. 27.6.4. Industrial Revenue Bonds
        5. 27.6.5. FHA-Insured Mortgage Hospital Bonds
          1. 27.6.5.1. What Are FHA Mortgage–Insured Hospital Bonds?
          2. 27.6.5.2. What Is the Credit Risk?
          3. 27.6.5.3. What Is the "Prudent Man" Evaluation Approach?
      7. 27.7. SUMMARY
    8. REFERENCES
  9. 4. Valuation
    1. 28. Introduction to Valuation
      1. 28.1. A PHILOSOPHICAL BASIS FOR VALUATION
      2. 28.2. GENERALITIES ABOUT VALUATION
        1. 28.2.1. Myth 1: Since Valuation Models Are Quantitative, Valuation Is Objective
          1. 28.2.1.1. The Biases in Equity Research
        2. 28.2.2. Myth 2: A Well-Researched and Well-Done Valuation Is Timeless
        3. 28.2.3. Myth 3: A Good Valuation Provides a Precise Estimate of Value
        4. 28.2.4. Myth 4: The More Quantitative a Model, the Better the Valuation
        5. 28.2.5. Myth 5: To Make Money on Valuation, You Have to Assume that Markets Are Inefficient
        6. 28.2.6. Myth 6: The Product of Valuation Is What Matters; The Process of Valuation Is Not Important
      3. 28.3. THE ROLE OF VALUATION
        1. 28.3.1. Valuation and Portfolio Management
          1. 28.3.1.1. Fundamental Analysts
          2. 28.3.1.2. Franchise Buyer
          3. 28.3.1.3. Chartists
          4. 28.3.1.4. Information Traders
          5. 28.3.1.5. Market Timers
          6. 28.3.1.6. Efficient Marketers
        2. 28.3.2. Valuation in Acquisition Analysis
        3. 28.3.3. Valuation in Corporate Finance
      4. 28.4. SUMMARY
    2. REFERENCES
    3. 29. Applied Equity Valuation: Discounted Cash Flow Method
      1. 29.1. DIVIDEND DISCOUNT MODEL
        1. 29.1.1. Stocks that Currently Pay No Dividend
      2. 29.2. CONSTANT-GROWTH DDM
      3. 29.3. NONCONSTANT-GROWTH DDM
      4. 29.4. INTUITION BEHIND THE DDM
      5. 29.5. COMPLICATIONS IN IMPLEMENTING THE DDM IN THE REAL WORLD
        1. 29.5.1. Expected Growth of Dividends
        2. 29.5.2. Appropriate Expected Required Rate of Return
        3. 29.5.3. Expected Future Selling Price
        4. 29.5.4. Reinvestment of Profits/Internal Financing that Support Growth
      6. 29.6. ADAPTING TO THE COMPLICATIONS: THE EARNINGS PER SHARE APPROACH
      7. 29.7. FREE CASH FLOW DCF MODEL—TOTAL FIRM VALUATION
        1. 29.7.1. Difference between Cash Flow and Free Cash Flow
      8. 29.8. CALCULATING FCF
      9. 29.9. USING THE CASH-FLOW STATEMENT TO ARRIVE AT OCF AND FCF
        1. 29.9.1. Adjustments for Changes in Net Working Capital
        2. 29.9.2. Adjustments for Investment in New Fixed Assets
        3. 29.9.3. Adjustments for Depreciation and Other Noncash Expenses
        4. 29.9.4. Financial Adjustments
      10. 29.10. VALUING THE TOTAL FIRM
      11. 29.11. ESTIMATING TOTAL FIRM VALUE USING THE FCF MODEL
      12. 29.12. SUMMARY
    4. REFERENCES
    5. 30. Applied Equity Valuation: Relative Valuation Method
      1. 30.1. THE BASIC PRINCIPLES OF RELATIVE VALUATION
      2. 30.2. STEPS IN RELATIVE VALUATION
        1. 30.2.1. Choose Similar (Comparable or Like-Kind) Firms
        2. 30.2.2. Choose Bases for Multiples
        3. 30.2.3. Determine an Appropriate Multiple
        4. 30.2.4. Project Bases for the Valued Firm
        5. 30.2.5. Value the Firm
      3. 30.3. SELECTING COMPARABLE FIRMS TO ESTIMATE AVERAGE MULTIPLES
      4. 30.4. CRITERIA MOST OFTEN USED FOR THE SELECTION OF COMPARABLE FIRMS
        1. 30.4.1. Industry Classification
        2. 30.4.2. Technology
        3. 30.4.3. Clientele
        4. 30.4.4. Size
        5. 30.4.5. Risk Class
      5. 30.5. DCF AND RV METHODS
        1. 30.5.1. When DCF Valuation Works Best
        2. 30.5.2. When RV Works Best
        3. 30.5.3. The Link between RV and DCF
        4. 30.5.4. Problems with Price/X Ratios (e.g., the P/E Ratio)
        5. 30.5.5. The Need for Sensitivity Analysis in Both DCF and RV—"What If" and Simulation
      6. 30.6. SUMMARY
    6. REFERENCES
    7. 31. Dividend Discount Models
      1. 31.1. DIVIDEND MEASURES
      2. 31.2. DIVIDENDS AND STOCK PRICES
      3. 31.3. BASIC DIVIDEND DISCOUNT MODELS
      4. 31.4. THE FINITE LIFE GENERAL DIVIDEND DISCOUNT MODEL
        1. 31.4.1. Assuming a Constant Discount Rate
        2. 31.4.2. Required Inputs
        3. 31.4.3. Assessing Relative Value
      5. 31.5. CONSTANT GROWTH DIVIDEND DISCOUNT MODEL
      6. 31.6. MULTIPHASE DIVIDEND DISCOUNT MODELS
        1. 31.6.1. Two-Stage Growth Model
        2. 31.6.2. Three-Stage Growth Model
      7. 31.7. STOCHASTIC DIVIDEND DISCOUNT MODELS
        1. 31.7.1. Binomial Stochastic Model
          1. 31.7.1.1. Binomial Additive Stochastic Model
          2. 31.7.1.2. Binomial Geometric Stochastic Model
        2. 31.7.2. Trinomial Stochastic Models
          1. 31.7.2.1. Trinomial Additive Stochastic Model
          2. 31.7.2.2. Trinomial Geometric Stochastic Model
        3. 31.7.3. Applications of the Stochastic DDM
          1. 31.7.3.1. Advantages of the Stochastic DDM
      8. 31.8. EXPECTED RETURNS AND DIVIDEND DISCOUNT MODELS
      9. 31.9. SUMMARY
    8. REFERENCES
    9. 32. Equity Analysis Using Traditional and Value-Based Metrics
      1. 32.1. OVERVIEW OF TRADITIONAL METRICS
        1. 32.1.1. Growth Rates
        2. 32.1.2. Return on Equity and the Dupont Formula
        3. 32.1.3. ROE and Leverage
        4. 32.1.4. Financial Risk Considerations
      2. 32.2. PRICE RELATIVES
        1. 32.2.1. Stock Analysis Using Price Multiples
        2. 32.2.2. Price Multiples: Comparables versus Forecasted Fundamentals
        3. 32.2.3. Price Relatives Using Common Factors
      3. 32.3. FUNDAMENTAL STOCK RETURN
      4. 32.4. REQUIRED RETURN: THE MISSING LINK
      5. 32.5. TRADITIONAL CAVEATS
      6. 32.6. OVERVIEW OF VALUE-BASED METRICS
        1. 32.6.1. Background
        2. 32.6.2. Basic EVA
        3. 32.6.3. EVA Spread
        4. 32.6.4. Return on Capital Decomposition
        5. 32.6.5. WACC Issues
          1. 32.6.5.1. Target Capital Structure
          2. 32.6.5.2. Estimating the Cost of Equity
          3. 32.6.5.3. Cash-Flow Return on Investment
        6. 32.6.6. Residual Income
        7. 32.6.7. Role of EVA Momentum
        8. 32.6.8. Valuation Considerations
          1. 32.6.8.1. Identifying Good Stocks
          2. 32.6.8.2. Residual Income Valuation
        9. 32.6.9. VBM Caveats
        10. 32.6.10. Case Study: Equity Analysis Template
      7. 32.7. SUMMARY
      8. 32.8. APPENDIX: CASE STUDY
        1. 32.8.1. Coca-Cola: Integrated Traditional and VBM Analyses
    10. REFERENCES
    11. 33. The Franchise Factor Approach to Firm Valuation
      1. 33.1. INTRODUCTION
      2. 33.2. BACKGROUND
        1. 33.2.1. Historical Data Observations
      3. 33.3. KEY FINDINGS
      4. 33.4. FORMULATION OF THE BASIC MODEL
      5. 33.5. P/E MYOPIA: THE FALLACY OF STABLE P/Es
        1. 33.5.1. P/E Orbits for High-Growth Stocks
        2. 33.5.2. P/E Orbits for Low-Growth Stocks
        3. 33.5.3. The Stable P/E
        4. 33.5.4. Two-Phase P/E Orbits
        5. 33.5.5. The Franchise Factor Model and P/E Orbits
          1. 33.5.5.1. FV Growth, FV Decay, and FV Bubbles
          2. 33.5.5.2. Franchise Valuation under Q-Type Competition
          3. 33.5.5.3. Franchise Labor
      6. 33.6. SUMMARY
    12. REFERENCES
    13. 34. IPO Valuation
      1. 34.1. LITERATURE REVIEW ON IPO VALUATION
      2. 34.2. ESTIMATION OF INTRINSIC IPO VALUE
      3. 34.3. COMPARABLE FIRM METHOD TO ESTIMATING INTRINSIC VALUE
        1. 34.3.1. Choosing Matching Firms
        2. 34.3.2. Calculating Comparable Firm Multiples
        3. 34.3.3. Empirical Evidence
      4. 34.4. REGRESSION METHOD TO ESTIMATING INTRINSIC VALUE
        1. 34.4.1. Independent Variables
        2. 34.4.2. Empirical Evidence
      5. 34.5. SUMMARY
    14. REFERENCES
    15. 35. The Valuation of Private Firms
      1. 35.1. THE STANDARD OF VALUE
      2. 35.2. WHAT IS BEING VALUED?
      3. 35.3. VALUATION METRICS
        1. 35.3.1. The Asset-Based Method
        2. 35.3.2. The Income Method
        3. 35.3.3. Market Method: The Method of Comparables
      4. 35.4. THE RELATIONSHIP BETWEEN A FIRM'S STAGE OF BUSINESS DEVELOPMENT AND THE VALUATION APPROACH
      5. 35.5. VALUING A PRIVATE FIRM
        1. 35.5.1. Overview of Tentex and Defining Cash Flow for Valuation Purposes
        2. 35.5.2. Compensation of Officers and Employee Family Members and Friends
        3. 35.5.3. Discretionary Expenses
        4. 35.5.4. The Fair Value of Tentex Based on Discounted Free Cash Flow to the Firm
        5. 35.5.5. Valuing Tentex: Discounted Free Cash Flow
        6. 35.5.6. Valuing Tentex Using Market Multiples
      6. 35.6. THE COST OF CAPITAL
        1. 35.6.1. The Cost of Equity
        2. 35.6.2. The Cost of Debt
      7. 35.7. DISCOUNT FOR LACK OF LIQUIDITY
      8. 35.8. SUMMARY
    16. REFERENCES
    17. 36. General Principles of Bond Valuation
      1. 36.1. GENERAL PRINCIPLES OF BOND VALUATION
        1. 36.1.1. Estimating Cash Flows
        2. 36.1.2. Determining the Appropriate Interest Rate or Rates
        3. 36.1.3. Discounting the Expected Cash Flows
        4. 36.1.4. Determining a Bond's Value
          1. 36.1.4.1. Valuing a Zero-Coupon Bond
          2. 36.1.4.2. Valuing a Bond between Coupon Payments
        5. 36.1.5. The Price/Discount Rate Relationship
        6. 36.1.6. Time Path of Bond
      2. 36.2. ARBITRAGE-FREE BOND VALUATION
        1. 36.2.1. Theoretical Spot Rates
          1. 36.2.1.1. Par Rates
          2. 36.2.1.2. Bootstrapping the Spot Rate Curve
        2. 36.2.2. Valuation Using Treasury Spot Rates
        3. 36.2.3. Reason for Using Treasury Spot Rates
        4. 36.2.4. Stripping and Arbitrage-Free Valuation
        5. 36.2.5. Credit Spreads and the Valuation of Non-Treasury Securities
      3. 36.3. SUMMARY
    18. REFERENCES
    19. 37. Yield Curves and Valuation Lattices
      1. 37.1. THE INTEREST RATE LATTICE
        1. 37.1.1. Determining the Value at a Node
      2. 37.2. CALIBRATING THE LATTICE
      3. 37.3. USING THE LATTICE FOR VALUATION
      4. 37.4. SUMMARY
    20. REFERENCES
    21. 38. Using the Lattice Model to Value Bonds with Embedded Options, Floaters, Options, and Caps/Floors
      1. 38.1. FIXED-COUPON BONDS WITH EMBEDDED OPTIONS
        1. 38.1.1. Valuing a Callable Bond
        2. 38.1.2. Valuing a Putable Bond
      2. 38.2. FLOATING-COUPON BONDS WITH EMBEDDED OPTIONS
        1. 38.2.1. Valuing Capped Floating-Rate Bonds
        2. 38.2.2. Callable Capped Floating-Rate Bonds
      3. 38.3. VALUING CAPS AND FLOORS
      4. 38.4. VALUATION OF TWO MORE EXOTIC STRUCTURES
        1. 38.4.1. Valuing a Step-Up Callable Note
        2. 38.4.2. Valuing a Range Note
      5. 38.5. VALUING AN OPTION ON A BOND
      6. 38.6. EXTENSIONS
        1. 38.6.1. Option-Adjusted Spread
        2. 38.6.2. Effective Duration and Effective Convexity
      7. 38.7. SUMMARY
    22. REFERENCES
    23. 39. Valuing Mortgage-Backed and Asset-Backed Securities
      1. 39.1. CASH-FLOW YIELD ANALYSIS
      2. 39.2. ZERO-VOLATILITY SPREAD
      3. 39.3. VALUATION USING MONTE CARLO SIMULATION AND OAS ANALYSIS
        1. 39.3.1. Simulating Interest Rate Paths and Cash Flows
        2. 39.3.2. Calculating the Present Value of a Bond Class for a Scenario Interest Rate Path
        3. 39.3.3. Determining the Theoretical Value
        4. 39.3.4. Option-Adjusted Spread
        5. 39.3.5. Option Cost
        6. 39.3.6. Simulated Average Life
      4. 39.4. MEASURING INTEREST RISK
        1. 39.4.1. Duration
        2. 39.4.2. Convexity
      5. 39.5. SUMMARY
    24. REFERENCES
    25. 40. A Framework for Valuing Treasury Inflation-Protected Securities
      1. 40.1. REVIEW OF TIPS STRUCTURE
      2. 40.2. ANALYSIS OF BREAKEVENS
        1. 40.2.1. Extracting Inflation Expectations from Breakevens
          1. 40.2.1.1. Convexity of TIPS and Nominal Rates
          2. 40.2.1.2. Risk Premium
          3. 40.2.1.3. Liquidity Premium
          4. 40.2.1.4. Inflation Expectations
      3. 40.3. SUMMARY
    26. REFERENCES
    27. 41. Quantitative Models to Value Convertible Bonds
      1. 41.1. ANALYTICAL MODELS
        1. 41.1.1. The Ingersoll Model
      2. 41.2. NUMERICAL MODELS
        1. 41.2.1. The Binomial Tree Model
      3. 41.3. SUMMARY
    28. REFERENCES
    29. 42. Introduction to the Pricing of Futures/Forwards and Options
      1. 42.1. PRICING OF FUTURES/FORWARD CONTRACTS
        1. 42.1.1. Differences between Futures and Forward Contracts
        2. 42.1.2. Basic Futures Pricing Model
        3. 42.1.3. A Closer Look at the Theoretical Futures Price
          1. 42.1.3.1. Interim Cash Flows
          2. 42.1.3.2. Differences in Borrowing and Lending Rates
          3. 42.1.3.3. Transaction Costs
          4. 42.1.3.4. Short Selling
          5. 42.1.3.5. Known Deliverable Asset and Settlement Date
          6. 42.1.3.6. Deliverable Is a Basket of Securities
          7. 42.1.3.7. Different Tax Treatment of Cash and Futures Transaction
      2. 42.2. PRICING OF OPTIONS
        1. 42.2.1. Basic Components of the Option Price
          1. 42.2.1.1. Intrinsic Value
          2. 42.2.1.2. Time Premium
        2. 42.2.2. Put–Call Parity Relationship
        3. 42.2.3. Factors that Influence the Option Price
          1. 42.2.3.1. Market Price of the Underlying Asset
          2. 42.2.3.2. Strike Price
          3. 42.2.3.3. Time to Expiration of the Option
          4. 42.2.3.4. Expected Volatility of the Underlying over the Life of the Option
          5. 42.2.3.5. Short-Term, Risk-Free Interest Rate over the Life of the Option
          6. 42.2.3.6. Anticipated Cash Payments on the Underlying over the Life of the Option
        4. 42.2.4. Option Pricing Models
      3. 42.3. SUMMARY
    30. REFERENCES
    31. 43. Black-Scholes Option Pricing Model
      1. 43.1. MOTIVATION
      2. 43.2. BLACK-SCHOLES FORMULA
      3. 43.3. COMPUTING A CALL OPTION PRICE
      4. 43.4. SENSITIVITY OF OPTION PRICE TO A CHANGE IN FACTORS: THE GREEKS
        1. 43.4.1. Price of a Call Option Price and Price of the Underlying: Delta and Gamma
        2. 43.4.2. The Call Option Price and Time to Expiration: Theta
        3. 43.4.3. Option Price and Expected Volatility: Vega
        4. 43.4.4. Call Option Price and Interest Rate: Rho
        5. 43.4.5. The Greeks and Portfolio Applications
      5. 43.5. COMPUTING A PUT OPTION PRICE
      6. 43.6. ASSUMPTIONS UNDERLYING THE BLACK-SCHOLES MODEL AND BASIC EXTENSIONS
        1. 43.6.1. Taxes and Transactions Costs
        2. 43.6.2. Trading in Continuous Time, Short Selling, and Trading Arbitrary Fractions of Assets
        3. 43.6.3. Variance of the Stock's Return
        4. 43.6.4. Stochastic Process Generating Stock Prices
        5. 43.6.5. Risk-Free Interest Rate
      7. 43.7. BLACK-SCHOLES MODEL APPLIED TO THE PRICING OF OPTIONS ON BONDS: IMPORTANCE OF ASSUMPTIONS
      8. 43.8. SUMMARY
    32. REFERENCES
    33. 44. Valuing a Plain Vanilla Swap
      1. 44.1. CALCULATING SWAP PAYMENTS
        1. 44.1.1. Calculating the Floating Payments
          1. 44.1.1.1. The Eurodollar Futures Contract
          2. 44.1.1.2. Determining Future Floating Payments
        2. 44.1.2. Calculating the Fixed Payments
        3. 44.1.3. Dealing with Swaps with a Varying Notional Principal
      2. 44.2. COMPUTING THE PRESENT VALUE OF SWAP PAYMENTS AND DETERMINING THE SWAP FIXED RATE
        1. 44.2.1. Calculating the Present Value of the Floating Payments
        2. 44.2.2. Determination of the Swap Fixed Rate
      3. 44.3. VALUING THE CASH FLOWS
        1. 44.3.1. Swap Floating Payments When Rates Change
        2. 44.3.2. Period Forward Rates and Forward Discount Factors after Rates Change
        3. 44.3.3. Valuing a Swap after Rates Change
      4. 44.4. SUMMARY
    34. REFERENCES
    35. 45. Valuing Swaptions
      1. 45.1. LATTICE APPROACH TO VALUATION
        1. 45.1.1. Binomial Interest Rate Lattice
        2. 45.1.2. Determining the Value at a Node
        3. 45.1.3. Constructing the Binomial Interest Rate Lattice
        4. 45.1.4. Obtaining the Cash Flow at Each Node of the Lattice
      2. 45.2. TYPES OF SWAPTIONS
      3. 45.3. ROLE OF THE CUMULATIVE SWAP VALUATION LATTICE
      4. 45.4. EXPIRATION VALUES AND THE SWAPTION VALUATION LATTICE
      5. 45.5. APPLYING THE BACKWARD INDUCTION METHODOLOGY TO OBTAIN A SWAPTION'S VALUE
      6. 45.6. FACTORS THAT AFFECT THE VALUE OF A SWAPTION
        1. 45.6.1. Expiration of the Swaption
        2. 45.6.2. Strike Rate
        3. 45.6.3. Assumed Interest Rate Volatility
        4. 45.6.4. Changes in the Term Structure
      7. 45.7. SUMMARY
    36. REFERENCES
    37. 46. Pricing Options on Interest Rate Instruments
      1. 46.1. MODELING THE TERM STRUCTURE AND BOND PRICES
        1. 46.1.1. Short-Rate Models of Term Interest Rate Structure
      2. 46.2. MODELING IN PRACTICE
      3. 46.3. HJM METHODOLOGY
      4. 46.4. BOND OPTION PRICING
        1. 46.4.1. European Options on the Money Fund
        2. 46.4.2. Options on Discount Bonds
          1. 46.4.2.1. Example: Valuing a Zero-Coupon Bond Call Option with the Vasicek Model
          2. 46.4.2.2. Example: Valuing a Zero-Coupon Bond Call Option with the Hull-White Model
          3. 46.4.2.3. Example: Valuing a Zero-Coupon Bond Call Option with the CIR Model
        3. 46.4.3. Options on Coupon-Paying Bonds
          1. 46.4.3.1. Example: Valuing a Coupon-Bond Call Option with the Vasicek Model
          2. 46.4.3.2. Example: Valuing a Coupon-Bond Call Option with the CIR Model
        4. 46.4.4. Pricing Swaptions
      5. 46.5. PRACTICAL CONSIDERATIONS
      6. 46.6. SUMMARY
    38. REFERENCES
    39. 47. Credit Default Swaps Valuation
      1. 47.1. DEFAULT SWAPS
        1. 47.1.1. Illustration
        2. 47.1.2. The Mechanics of Settlement
      2. 47.2. CREDIT EVENTS
        1. 47.2.1. ISDA Credit Event Definitions
        2. 47.2.2. Restructuring Controversy
        3. 47.2.3. Credit Events and Implementation of Default Swap Pricing Models
      3. 47.3. PRICING CREDIT DEFAULT SWAPS BY STATIC REPLICATION
      4. 47.4. PRICING OF A SINGLE-NAME CREDIT DEFAULT SWAP
        1. 47.4.1. Survival Probability
        2. 47.4.2. Valuation of a Credit Default Swap
        3. 47.4.3. CDS Risk and Sensitivities
        4. 47.4.4. Calibrating the Recovery Rate Assumption
        5. 47.4.5. The Practicalities of Unwinding a Credit Default Swap
      5. 47.5. SUMMARY
    40. REFERENCES
    41. 48. The Valuation of Fixed Income Total Return Swaps
      1. 48.1. AN INTUITIVE APPROACH
      2. 48.2. USING THE DUFFIE-SINGLETON MODEL
      3. 48.3. THE FORWARD MEASURE
      4. 48.4. SUMMARY
    42. REFERENCES
    43. 49. Valuing Inflation Derivatives
      1. 49.1. INFLATION INDICES AND REAL RETURNS
      2. 49.2. VALUING ZERO-COUPON INFLATION SWAPS
      3. 49.3. CONSTRUCTING AN INFLATION CURVE
        1. 49.3.1. Incorporating Seasonality Effects
      4. 49.4. MARKING TO MARKET INFLATION SWAPS
      5. 49.5. MANAGING INFLATION AND INTEREST RATE RISK
        1. 49.5.1. Inflation PV01
        2. 49.5.2. Nominal PV01
      6. 49.6. MANAGING SEASONALITY RISK
      7. 49.7. THE JARROW-YILDIRIM MODEL
      8. 49.8. VALUATION OF PERIOD-ON-PERIOD INFLATION SWAPS
      9. 49.9. VALUATION OF INFLATION INDEX OPTIONS
      10. 49.10. VALUATION OF INFLATION OPTIONS
      11. 49.11. VALUATION OF REAL RATE INFLATION SWAPTIONS
      12. 49.12. VALUATION OF INFLATION-EQUITY HYBRID
      13. 49.13. SUMMARY
    44. REFERENCES
    45. 50. The Pricing and Economics of Commodity Futures
      1. 50.1. THE RELATIONSHIP BETWEEN FUTURES PRICES AND SPOT PRICES
        1. 50.1.1. Financial Futures
        2. 50.1.2. Currencies
        3. 50.1.3. Commodity Futures
      2. 50.2. ECONOMICS OF THE COMMODITY MARKETS: NORMAL BACKWARDATION VERSUS CONTANGO
      3. 50.3. COMMODITY PRICES COMPARED TO FINANCIAL ASSET PRICES
      4. 50.4. SUMMARY
    46. REFERENCES
    47. 51. Introduction to Currency Option Pricing Models
      1. 51.1. BASIC PROPERTIES
      2. 51.2. THEORETICAL VALUATION
      3. 51.3. BLACK-SCHOLES MODEL
      4. 51.4. EXAMPLES OF OTHER MODELS
      5. 51.5. PRICING WITHOUT A COMPUTER MODEL
        1. 51.5.1. Educated Guess
      6. 51.6. THE PRICE OF AN OPTION
        1. 51.6.1. Option Premium Profile
          1. 51.6.1.1. Time Value and Intrinsic Value
          2. 51.6.1.2. Time to Expiry
          3. 51.6.1.3. Volatility
          4. 51.6.1.4. Strike Price and Forward Rates
          5. 51.6.1.5. Interest Rates
          6. 51.6.1.6. American versus European
      7. 51.7. THE GREEKS
        1. 51.7.1. Delta
        2. 51.7.2. Gamma
        3. 51.7.3. Theta
        4. 51.7.4. Vega
        5. 51.7.5. Rho
        6. 51.7.6. Beta and Omega
      8. 51.8. SUMMARY
    48. REFERENCES
    49. 52. Pricing Commercial Real Estate Derivatives
      1. 52.1. PRICING THE FORWARD CONTRACT
      2. 52.2. PRICING A REAL ESTATE INDEX RETURN SWAP: EQUILIBRIUM ANALYSIS
        1. 52.2.1. Numerical Example
      3. 52.3. SUMMARY
    50. REFERENCES
  10. 5. Mathematical Tools and Techniques for Financial Modeling and Analysis
    1. 53. Cash-Flow Analysis
      1. 53.1. DIFFICULTIES WITH MEASURING CASH FLOW
      2. 53.2. CASH FLOWS AND THE STATEMENT OF CASH FLOWS
      3. 53.3. FREE CASH FLOW
      4. 53.4. CALCULATING FREE CASH FLOW
      5. 53.5. NET FREE CASH FLOW
      6. 53.6. USEFULNESS OF CASH FLOWS IN FINANCIAL ANALYSIS
        1. 53.6.1. Ratio Analysis
        2. 53.6.2. Using Cash-Flow Information
      7. 53.7. SUMMARY
    2. REFERENCES
    3. 54. Financial Ratio Analysis
      1. 54.1. RATIOS AND THEIR CLASSIFICATION
      2. 54.2. RETURN-ON-INVESTMENT RATIOS
        1. 54.2.1. Recap: Return-on-Investment Ratios
        2. 54.2.2. DuPont System
      3. 54.3. LIQUIDITY
        1. 54.3.1. Operating Cycle
        2. 54.3.2. Measures of Liquidity
        3. 54.3.3. Recap: Liquidity Ratios
      4. 54.4. PROFITABILITY RATIOS
        1. 54.4.1. Recap: Profitability Ratios
      5. 54.5. ACTIVITY RATIOS
        1. 54.5.1. Inventory Management
        2. 54.5.2. Accounts Receivable Management
        3. 54.5.3. Overall Asset Management
        4. 54.5.4. Recap: Activity Ratios
      6. 54.6. FINANCIAL LEVERAGE RATIOS
        1. 54.6.1. Component Percentage Ratios
          1. 54.6.1.1. Book Value versus Market Value
        2. 54.6.2. Coverage Ratios
        3. 54.6.3. Recap: Financial Leverage Ratios
      7. 54.7. COMMON-SIZE ANALYSIS
      8. 54.8. USING FINANCIAL RATIO ANALYSIS
      9. 54.9. SUMMARY
    4. REFERENCES
    5. 55. Mathematics of Finance
      1. 55.1. THE IMPORTANCE OF THE TIME VALUE OF MONEY
      2. 55.2. DETERMINING THE FUTURE VALUE
        1. 55.2.1. Compounding More than One Time per Year
        2. 55.2.2. Continuous Compounding
        3. 55.2.3. Multiple Rates
      3. 55.3. DETERMINING THE PRESENT VALUE
      4. 55.4. DETERMINING THE UNKNOWN INTEREST RATE
      5. 55.5. DETERMINING THE NUMBER OF COMPOUNDING PERIODS
      6. 55.6. THE TIME VALUE OF A SERIES OF CASH FLOWS
        1. 55.6.1. Shortcuts: Annuities
      7. 55.7. VALUING CASH FLOWS WITH DIFFERENT TIME PATTERNS
        1. 55.7.1. Valuing a Perpetual Stream of Cash Flows
        2. 55.7.2. Valuing an Annuity Due
        3. 55.7.3. Valuing a Deterred Annuity
      8. 55.8. LOAN AMORTIZATION
      9. 55.9. THE CALCULATION OF INTEREST RATES AND YIELDS
        1. 55.9.1. Annual Percentage Rate versus Effective Annual Rate
        2. 55.9.2. Yields on Investments
      10. 55.10. SUMMARY
    6. REFERENCES
    7. 56. Calculating Investment Returns
      1. 56.1. SINGLE-PERIOD RATE OF RETURN
        1. 56.1.1. Components of Single-Period Returns
        2. 56.1.2. Return on Investment
      2. 56.2. TIME VALUE OF MONEY
        1. 56.2.1. Returns That Take Time into Account
      3. 56.3. PERFORMANCE OF THE INVESTOR: MONEY-WEIGHTED RETURNS
        1. 56.3.1. Timing of Investor Decisions
        2. 56.3.2. Timing of Investment Manager Decisions
        3. 56.3.3. Segregating Investor and Manager Timing Decisions
        4. 56.3.4. Internal Rate of Return
        5. 56.3.5. Problems with the IRR
        6. 56.3.6. Modified Dietz Return
      4. 56.4. PERFORMANCE OF THE INVESTMENT MANAGER: TIME-WEIGHTED RETURNS
        1. 56.4.1. Time-Weighted Return
          1. 56.4.1.1. Divide the Period into Subperiods
          2. 56.4.1.2. Calculate Subperiod Returns
          3. 56.4.1.3. Calculate Multiple-Period Returns
        2. 56.4.2. Estimating the Time-Weighted Return
      5. 56.5. MULTIPLE-PERIOD RETURN CALCULATION
        1. 56.5.1. Cumulative Returns
        2. 56.5.2. Averaging Returns
        3. 56.5.3. Geometric Mean Return
        4. 56.5.4. Annualizing Returns
      6. 56.6. SUMMARY
    8. REFERENCES
    9. 57. Basic Data Description for Financial Modeling and Analysis
      1. 57.1. DATA TYPES
        1. 57.1.1. Information Contained in the Data
        2. 57.1.2. Data Levels and Scale
        3. 57.1.3. Cross-Sectional Data and Time Series
      2. 57.2. FREQUENCY DISTRIBUTIONS
        1. 57.2.1. Sorting and Counting Data
        2. 57.2.2. Formal Presentation of Frequency
      3. 57.3. EMPIRICAL CUMULATIVE FREQUENCY DISTRIBUTION
        1. 57.3.1. Accumulating Frequencies
        2. 57.3.2. Formal Presentation of Cumulative Frequency Distributions
      4. 57.4. DATA CLASSES
        1. 57.4.1. Reasons for Classifying
        2. 57.4.2. Formal Procedure of Classifying
        3. 57.4.3. Example of Classing Procedures
      5. 57.5. CUMULATIVE FREQUENCY DISTRIBUTIONS
      6. 57.6. SUMMARY
    10. REFERENCES
    11. 58. Elementary Statistics
      1. 58.1. POPULATION VERSUS SAMPLE
        1. 58.1.1. Summary of the Statistical Method
      2. 58.2. RANDOM VARIABLES
        1. 58.2.1. Mean
        2. 58.2.2. Variance and Standard Deviation
        3. 58.2.3. Covariance and Correlation
        4. 58.2.4. Semivariance and Semistandard Deviation
        5. 58.2.5. Semicovariance and Semicorrelation
        6. 58.2.6. Skewness
        7. 58.2.7. Kurtosis
      3. 58.3. PROPERTIES OF EXPECTATION OPERATORS
      4. 58.4. ESTIMATION
        1. 58.4.1. Estimator of Mean
        2. 58.4.2. Estimator of Variance
        3. 58.4.3. Estimator of Covariance and Correlation
        4. 58.4.4. Estimator of Lower Semivariance
        5. 58.4.5. Estimators of Semicovariance and Semicorrelation
        6. 58.4.6. Estimator of Skewness
        7. 58.4.7. Estimator of Kurtosis
        8. 58.4.8. Illustration: Estimate of Mean, Variance, Standard Deviation, Skewness, and Excess Kurtosis of Monthly Stock Returns for IBM
      5. 58.5. PROBABILITY DISTRIBUTIONS
        1. 58.5.1. Normal Distribution
          1. 58.5.1.1. Empirical Distribution
          2. 58.5.1.2. Normal Distribution
        2. 58.5.2. Chi-Square Distribution
          1. 58.5.2.1. Tests for Normality
        3. 58.5.3. t-Distribution
          1. 58.5.3.1. Test for Zero Mean
          2. 58.5.3.2. Test for Equivalence of Means
          3. 58.5.3.3. Test for Equivalence of Means in a Paired Sample
        4. 58.5.4. Type I and Type II Errors and the Power of a Test
        5. 58.5.5. F-Distribution
          1. 58.5.5.1. Test for Equivalence of Variances
        6. 58.5.6. Test for Autocorrelation
        7. 58.5.7. Central Limit Theorem
      6. 58.6. SUMMARY
    12. REFERENCES
    13. A. DATA FOR ILLUSTRATION
    14. B. Statistical Tables
    15. 59. Regression Analysis
      1. 59.1. THE CONCEPT OF DEPENDENCE
      2. 59.2. REGRESSIONS AND LINEAR MODELS
        1. 59.2.1. Case Where All Regressors Are Random Variables
        2. 59.2.2. Linear Models and Linear Regressions
        3. 59.2.3. Case Where Regressors Are Deterministic Variables
      3. 59.3. ESTIMATION OF LINEAR REGRESSIONS
        1. 59.3.1. Maximum Likelihood Estimates
          1. 59.3.1.1. Generalization to Multiple Independent Variables
        2. 59.3.2. Ordinary Least Squares Method
      4. 59.4. SAMPLING DISTRIBUTIONS OF REGRESSIONS
      5. 59.5. DETERMINING THE EXPLANATORY POWER OF A REGRESSION
        1. 59.5.1. Coefficient of Determination
        2. 59.5.2. Adjusted R2
        3. 59.5.3. Relation of R2 to Correlation Coefficient
      6. 59.6. USING REGRESSION ANALYSIS IN FINANCE
        1. 59.6.1. Characteristic Line for Common Stocks
        2. 59.6.2. Characteristic Line for Mutual Funds
        3. 59.6.3. Empirical Duration of Common Stock
      7. 59.7. STEPWISE REGRESSION
      8. 59.8. NONNORMALITY AND AUTOCORRELATION OF THE RESIDUALS
        1. 59.8.1. Detecting Autocorrelation
      9. 59.9. PITFALLS OF REGRESSIONS
        1. 59.9.1. Spurious Regressions
        2. 59.9.2. Collinearity
        3. 59.9.3. Increasing the Number of Regressors
      10. 59.10. SUMMARY
      11. 59.11. ACKNOWLEDGMENTS
    16. REFERENCES
    17. 60. ARCH/GARCH Models in Applied Financial Econometrics
      1. 60.1. REVIEW OF LINEAR REGRESSION AND AUTOREGRESSIVE MODELS
      2. 60.2. ARCH/GARCH MODELS
        1. 60.2.1. Application to Value at Risk
      3. 60.3. WHY ARCH/GARCH?
      4. 60.4. GENERALIZATIONS OF THE ARCH/GARCH MODELS
        1. 60.4.1. Integration of First, Second, and Higher Moments
        2. 60.4.2. Generalizations to High-Frequency Data
        3. 60.4.3. Multivariate Extensions
      5. 60.5. SUMMARAY
    18. REFERENCES
    19. 61. Cointegration and Its Application in Finance
      1. 61.1. STATIONARY AND NONSTATIONARY VARIABLES AND COINTEGRATION
      2. 61.2. TESTING FOR COINTEGRATION
        1. 61.2.1. Engle-Granger Cointegration Tests
      3. 61.3. EMPIRICAL ILLUSTRATION USING THE DIVIDEND GROWTH MODEL
        1. 61.3.1. Johansen-Juselius Cointegration Tests
      4. 61.4. TESTING OF THE DYNAMIC RELATIONSHIPS AMONG COUNTRY STOCK MARKETS
      5. 61.5. SUMMARY
    20. REFERENCES
    21. 62. Moving Average Models for Volatility and Correlation, and Covariance Matrices
      1. 62.1. BASIC PROPERTIES OF COVARIANCE AND CORRELATION MATRICES
      2. 62.2. EQUALLY WEIGHTED AVERAGES
        1. 62.2.1. Statistical Methodology
        2. 62.2.2. Confidence Intervals for Variance and Volatility
        3. 62.2.3. Standard Errors for Equally Weighted Average Estimators
        4. 62.2.4. Equally Weighted Moving Average Covariance Matrices
        5. 62.2.5. Case Study: Measuring the Volatility and Correlation of U.S Treasuries
          1. 62.2.5.1. Decision 1: How Long a Historical Data Period Should Be Used?
          2. 62.2.5.2. Decision 2: Which Frequency of Observations Should Be Used?
          3. 62.2.5.3. Decision 3: Absolute versus Relative Measures
        6. 62.2.6. Pitfalls of the Equally Weighted Moving Average Method
        7. 62.2.7. Using Equally Weighted Moving Averages
      3. 62.3. EXPONENTIALLY WEIGHTED MOVING AVERAGES
        1. 62.3.1. Statistical Methodology
        2. 62.3.2. Interpretation of λ
        3. 62.3.3. Properties of the Estimates
        4. 62.3.4. The EWMA Forecasting Model
        5. 62.3.5. Standard Errors for EWMA Forecasts
        6. 62.3.6. The RiskMetricsTM Methodology
      4. 62.4. SUMMARY
    22. REFERENCES
    23. 63. Introduction to Stochastic Processes
      1. 63.1. STOCHASTIC PROCESSES IN DISCRETE TIME
        1. 63.1.1. Autoregressive Moving Average Models
          1. 63.1.1.1. White Noise
          2. 63.1.1.2. Autoregressive Processes
          3. 63.1.1.3. Moving Average Processes
          4. 63.1.1.4. Autoregressive Moving Average Processes with Exogenous Variables
        2. 63.1.2. Summary of Properties of Linear Time Series Models
      2. 63.2. ARCH and GARCH Models
      3. 63.3. STOCHASTIC PROCESSES IN CONTINUOUS TIME
        1. 63.3.1. The Poisson Process
          1. 63.3.1.1. Transforms of the Poisson Process
        2. 63.3.2. Brownian Motion
          1. 63.3.2.1. Transforms of Brownian Motion
          2. 63.3.2.2. Fractional Brownian Motion
        3. 63.3.3. Stochastic Differential Equations
        4. 63.3.4. Lévy Processes
          1. 63.3.4.1. α-Stable Lévy Motion
      4. 63.4. SUMMARY
    24. REFERENCES
    25. 64. Bayesian Probability for Investors
      1. 64.1. CONCEPT AND CONTEXT
        1. 64.1.1. Fundamental Bayesian Concepts
          1. 64.1.1.1. The Laws of Probability
          2. 64.1.1.2. Probability Distributions
          3. 64.1.1.3. A Second Level of Abstraction
        2. 64.1.2. Predictions
        3. 64.1.3. Origins, Diffusion, and Elaboration
          1. 64.1.3.1. Bayesian Approaches Become Respectable
          2. 64.1.3.2. Modern Bayesians
          3. 64.1.3.3. Notable Investment Examples
      2. 64.2. BAYES ON A SPREADSHEET
        1. 64.2.1. Summarizing Simple Evidence condition
          1. 64.2.1.1. Quantifying the Qualitative
          2. 64.2.1.2. Estimating a Probability from Sequences of Binomial Data
          3. 64.2.1.3. Back to our Canadian Farmland Questions
          4. 64.2.1.4. Longer Sequences of Evidence
        2. 64.2.2. Intuition for Blending Priors and Likelihoods
        3. 64.2.3. When Quantifying Scale Is Critical
        4. 64.2.4. The Normal, Scaled Inverse Chi-Squared Joint Distribution
        5. 64.2.5. Back to our Value-Oriented Active Management Question
      3. 64.3. SOME PROGRAMMING REQUIRED
        1. 64.3.1. Taking Advantage of Group Relations
          1. 64.3.1.1. Creating Exchangeable Individuals
          2. 64.3.1.2. Procedure
          3. 64.3.1.3. Getting to τ
          4. 64.3.1.4. Inferring the Distribution for µ
          5. 64.3.1.5. Inferring the Distributions for Each Individual Mean
          6. 64.3.1.6. The Result for Our Mutual Fund Study
          7. 64.3.1.7. With More Advanced Techniques
          8. 64.3.1.8. Thinking about Other Applications of Hierarchical Models
        2. 64.3.2. Improving Markowitz Mean-Variance Optimization
        3. 64.3.3. Harnessing Advanced Techniques
      4. 64.4. ADDITIONAL RELATED WORK
      5. 64.5. SUMMARY
    26. REFERENCES
    27. 65. Monte Carlo Simulation in Finance
      1. 65.1. MAIN IDEAS AND IMPORTANT CONCEPTS
        1. 65.1.1. How Many Scenarios?
        2. 65.1.2. Estimator Bias
        3. 65.1.3. Estimator Efficiency
      2. 65.2. FINANCIAL APPLICATIONS OF SIMULATION
        1. 65.2.1. Financial Derivative Pricing
        2. 65.2.2. Estimating Sensitivities
        3. 65.2.3. Protfolio Risk Management
        4. 65.2.4. Valuing Mortgage-Backed Securities
        5. 65.2.5. Valuing Credit-Risky Securities
      3. 65.3. RANDOM NUMBER GENERATION
        1. 65.3.1. From a Uniform Random Variable to a Variable from an Arbitrary Distribution
        2. 65.3.2. What Defines a "Good" Random Number Generator?
        3. 65.3.3. Pseudo-Random Numbers Generators
      4. 65.4. VARIANCE REDUCTION TECHNIQUES
        1. 65.4.1. Antithetic Variables
        2. 65.4.2. Stratified Sampling
        3. 65.4.3. Importance Sampling
        4. 65.4.4. Quasi-Random (Low-Discrepancy) Sequences
      5. 65.5. SIMULATION SOFTWARE
      6. 65.6. SUMMARY
    28. REFERENCES
    29. 66. Principles of Optimization for Portfolio Selection
      1. 66.1. UNCONSTRAINED OPTIMIZATION
        1. 66.1.1. Minima and Maxima of a Differentiable Function
        2. 66.1.2. Convex Functions
        3. 66.1.3. Quasi-Convex Functions
      2. 66.2. CONSTRAINED OPTIMIZATION
        1. 66.2.1. Lagrange Multipliers
        2. 66.2.2. Convex Programming
        3. 66.2.3. Linear Programming
        4. 66.2.4. Quadratic Programming
      3. 66.3. SUMMARY
    30. REFERENCES
    31. 67. Introduction to Stochastic Programming and Its Applications to Finance
      1. 67.1. WHAT IS STOCHASTIC PROGRAMMING?
        1. 67.1.1. Stochastic Programming in Finance
      2. 67.2. STOCHASTIC PROGRAMMING VERSUS OTHER METHODS IN FINANCE
        1. 67.2.1. Static versus Dynamic Models in Financial Planning
        2. 67.2.2. Continuous-Time Models versus Stochastic Programming
      3. 67.3. A GENERAL MULTISTAGE STOCHASTIC PROGRAMMING MODEL FOR FINANCIAL PLANNING
        1. 67.3.1. Model Formulation
          1. 67.3.1.1. Parameters
          2. 67.3.1.2. Decision Variables
        2. 67.3.2. Modeling Future Uncertainties (Scenario Generation)
      4. 67.4. SUMMARY
    32. REFERENCES
    33. 68. Robust Portfolio Optimization
      1. 68.1. THE ROBUST OPTIMIZATION APPROACH
        1. 68.1.1. Selecting Uncertainty Sets from Statistical Procedures
        2. 68.1.2. Clarifying a Misconception about Robust Optimization
      2. 68.2. THE RELATIONSHIP TO BAYESIAN METHODS AND ECONOMIC THEORY
      3. 68.3. USING ROBUST PORTFOLIO OPTIMIZATION IN PRACTICE
        1. 68.3.1. Effect of Robust Portfolio Optimization Formulations on Performance
      4. 68.4. PRACTICAL CONSIDERATIONS FOR ROBUST PORTFOLIO ALLOCATION
      5. 68.5. FUTURE DIRECTIONS
      6. 68.6. SUMMARY
    34. REFERENCES