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Encyclopedia of Financial Models III

Book Description

An essential reference dedicated to a wide array of financial models, issues in financial modeling, and mathematical and statistical tools for financial modeling

The need for serious coverage of financial modeling has never been greater, especially with the size, diversity, and efficiency of modern capital markets. With this in mind, the Encyclopedia of Financial Models, 3 Volume Set has been created to help a broad spectrum of individuals—ranging from finance professionals to academics and students—understand financial modeling and make use of the various models currently available.

Incorporating timely research and in-depth analysis, the Encyclopedia of Financial Models is an informative 3-Volume Set that covers both established and cutting-edge models and discusses their real-world applications. Edited by Frank Fabozzi, this set includes contributions from global financial experts as well as academics with extensive consulting experience in this field. Organized alphabetically by category, this reliable resource consists of three separate volumes and 127 entries—touching on everything from asset pricing and bond valuation models to trading cost models and volatility—and provides readers with a balanced understanding of today's dynamic world of financial modeling.

  • This 3-Volume Set contains coverage of the fundamentals and advances in financial modeling and provides the mathematical and statistical techniques needed to develop and test financial models

  • Emphasizes both technical and implementation issues, providing researchers, educators, students, and practitioners with the necessary background to deal with issues related to financial modeling

  • Each volume includes a complete table of contents and index for easy access to various parts of the encyclopedia

Financial models have become increasingly commonplace, as well as complex. They are essential in a wide range of financial endeavors, and this 3-Volume Set will help put them in perspective.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. About the Editor
  5. Contributors
  6. Preface
    1. TOPIC CATEGORIES
  7. Guide to the Encyclopedia of Financial Models
    1. Organization
  8. Mortgage-Backed Securities Analysis and Valuation
    1. Valuing Mortgage-Backed and Asset-Backed Securities
      1. CASH-FLOW YIELD ANALYSIS
      2. ZERO-VOLATILITY SPREAD
      3. VALUATION USING MONTE CARLO SIMULATION AND OAS ANALYSIS
      4. MEASURING INTEREST RISK
      5. KEY POINTS
      6. NOTES
    2. The Active-Passive Decomposition Model for MBS
      1. PATH-DEPENDENCE AND PRICING PARTIAL DIFFERENTIAL EQUATION
      2. EXTENDED ACTIVE-PASSIVE DECOMPOSITION MODEL
      3. EXTENSIONS AND NUANCES
      4. KEY POINTS
      5. NOTES
    3. Analysis of Nonagency Mortgage-Backed Securities
      1. FACTORS IMPACTING RETURNS FROM NONAGENCY MBS
      2. UNDERSTANDING THE EVOLUTION OF CREDIT PERFORMANCE WITHIN A TRANSACTION
      3. THE PROCESS OF ESTIMATING PRIVATE-LABEL MBS RETURNS
      4. KEY POINTS
      5. NOTES
    4. Measurement of Prepayments for Residential Mortgage-Backed Securities
      1. PREPAYMENT TERMINOLOGY
      2. CALCULATING PREPAYMENT SPEEDS
      3. DELINQUENCY, DEFAULT, AND LOSS TERMINOLOGY
      4. KEY POINTS
      5. NOTES
    5. Prepayments and Factors Influencing the Return of Principal for Residential Mortgage-Backed Securities
      1. PREPAYMENT FUNDAMENTALS
      2. FACTORS INFLUENCING PREPAYMENT SPEEDS
      3. DEFAULTS AND “INVOLUNTARY” PREPAYMENTS
      4. KEY POINTS
      5. NOTES
  9. Operational Risk
    1. Operational Risk
      1. Operational Risk Defined
      2. OPERATIONAL RISK EXPOSURE INDICATORS
      3. CLASSIFICATION OF OPERATIONAL RISK
      4. KEY POINTS
      5. NOTES
    2. Operational Risk Models
      1. OPERATIONAL RISK MODELS
      2. Specifics of Operational Loss Data
      3. KEY POINTS
      4. NOTES
    3. Modeling Operational Loss Distributions
      1. APPROACHES TO OPERATIONAL RISK MODELING
      2. NONPARAMETRIC APPROACH: EMPIRICAL DISTRIBUTION FUNCTION
      3. PARAMETRIC APPROACH: CONTINUOUS LOSS DISTRIBUTIONS
      4. EXTENSION: MIXTURE LOSS DISTRIBUTIONS
      5. A NOTE ON THE TAIL BEHAVIOR
      6. EMPIRICAL EVIDENCE WITH OPERATIONAL LOSS DATA
      7. KEY POINTS
      8. NOTES
  10. Optimization Tools
    1. Introduction to Stochastic Programming and Its Applications to Finance
      1. WHAT IS STOCHASTIC PROGRAMMING?
      2. STOCHASTIC PROGRAMMING VERSUS OTHER METHODS IN FINANCE
      3. A GENERAL MULTISTAGE STOCHASTIC PROGRAMMING MODEL FOR FINANCIAL PLANNING
      4. KEY POINTS
    2. Robust Portfolio Optimization
      1. THE ROBUST OPTIMIZATION APPROACH
      2. THE RELATIONSHIP TO BAYESIAN METHODS AND ECONOMIC THEORY
      3. USING ROBUST PORTFOLIO OPTIMIZATION IN PRACTICE
      4. PRACTICAL CONSIDERATIONS FOR ROBUST PORTFOLIO ALLOCATION
      5. FUTURE DIRECTIONS
      6. KEY POINTS
  11. Probability Theory
    1. Concepts of Probability Theory
      1. HISTORICAL DEVELOPMENT OF ALTERNATIVE APPROACHES TO PROBABILITY
      2. SET OPERATIONS AND PRELIMINARIES
      3. PROBABILITY MEASURE
      4. RANDOM VARIABLE
      5. KEY POINTS
      6. NOTES
    2. Discrete Probability Distributions
      1. DISCRETE LAW
      2. BERNOULLI DISTRIBUTION
      3. BINOMIAL DISTRIBUTION
      4. HYPERGEOMETRIC DISTRIBUTION
      5. MULTINOMIAL DISTRIBUTION
      6. POISSON DISTRIBUTION
      7. DISCRETE UNIFORM DISTRIBUTION
      8. APPENDIX B Binomial and Multinomial Coefficients
      9. BINOMIAL COEFFICIENT
      10. MULTINOMIAL COEFFICIENT
      11. KEY POINTS
      12. NOTE
    3. Continuous Probability Distributions
      1. CONTINUOUS PROBABILITY DISTRIBUTION DESCRIBED
      2. DISTRIBUTION FUNCTION
      3. DENSITY FUNCTION
      4. CONTINUOUS RANDOM VARIABLE
      5. COMPUTING PROBABILITIES FROM THE DENSITY FUNCTION
      6. LOCATION PARAMETERS
      7. DISPERSION PARAMETERS
      8. KEY POINTS
      9. NOTES
    4. Continuous Probability Distributions with Appealing Statistical Properties
      1. NORMAL DISTRIBUTION
      2. CHI-SQUARE DISTRIBUTION
      3. STUDENT'S t-DISTRIBUTION
      4. F-DISTRIBUTION
      5. EXPONENTIAL DISTRIBUTION
      6. RECTANGULAR DISTRIBUTION
      7. GAMMA DISTRIBUTION
      8. BETA DISTRIBUTION
      9. LOG-NORMAL DISTRIBUTION
      10. KEY POINTS
      11. NOTES
    5. Continuous Probability Distributions Dealing with Extreme Events
      1. GENERALIZED EXTREME VALUE DISTRIBUTION
      2. GENERALIZED PARETO DISTRIBUTION
      3. NORMAL INVERSE GAUSSIAN DISTRIBUTION
      4. α-STABLE DISTRIBUTION
      5. KEY POINTS
    6. Stable and Tempered Stable Distributions
      1. α-STABLE DISTRIBUTION
      2. TEMPERED STABLE DISTRIBUTIONS
      3. INFINITELY DIVISIBLE DISTRIBUTIONS
      4. HYPERGEOMETRIC FUNCTION AND CONFLUENT HYPERGEOMETRIC FUNCTION
      5. KEY POINTS
      6. NOTES
    7. Fat Tails, Scaling, and Stable Laws
      1. SCALING, STABLE LAWS, AND FAT TAILS
      2. EXTREME VALUE THEORY FOR IID PROCESSES
      3. ELIMINATING THE ASSUMPTION OF IID SEQUENCES
      4. KEY POINTS
      5. NOTES
    8. Copulas
      1. DRAWBACKS OF CORRELATION
      2. OVERCOMING THE DRAWBACKS OF CORRELATION: COPULAS
      3. MATHEMATICAL DEFINITION OF COPULAS
      4. KEY POINTS
      5. NOTES
    9. Applications of Order Statistics to Risk Management Problems
      1. PERFORMANCE OF VaR ESTIMATION
      2. VaR AND DIFFERENT LEVELS OF CONFIDENCE
      3. JOINT PROBABILITY DISTRIBUTIONS FOR ORDER STATISTICS
      4. DISTRIBUTION-FREE CONFIDENCE INTERVALS FOR VaR
      5. BIVARIATE ORDER STATISTICS
      6. KEY POINTS
      7. NOTE
  12. Risk Measures
    1. Measuring Interest Rate Risk: Effective Duration and Convexity
      1. EFFECTIVE DURATION AND EFFECTIVE CONVEXITY AN EXAMPLE
      2. PUTTING IT ALL TOGETHER
      3. KEY POINTS
      4. NOTES
    2. Yield Curve Risk Measures
      1. DURATION, CONVEXITY, AND NONPARALLEL YIELD CURVE SHIFTS
      2. CASH-FLOW DISTRIBUTION ANALYSIS VERSUS A BENCHMARK
      3. KEY RATE DURATION
      4. SLOPE ELASTICITY MEASURE
      5. YIELD CURVE RESHAPING DURATION
      6. ANALYSIS OF LIKELY YIELD CURVE SHIFTS
      7. KEY POINTS
      8. NOTE
    3. Value-at-Risk
      1. VALUE-AT-RISK DEFINED
      2. COMPUTING PORTFOLIO VaR IN PRACTICE
      3. BACK-TESTING OF VaR
      4. COHERENT RISK MEASURES
      5. KEY POINTS
      6. NOTES
    4. Average Value-at-Risk
      1. AVERAGE VALUE-AT-RISK DEFINED
      2. AVaR ESTIMATION FROM A SAMPLE
      3. COMPUTING PORTFOLIO AVAR IN PRACTICE
      4. BACK-TESTING OF AVaR
      5. TECHNICAL APPENDIX
      6. KEY POINTS
      7. NOTES
    5. Risk Measures and Portfolio Selection
      1. DESIRABLE FEATURES OF INVESTMENT RISK MEASURES
      2. ALTERNATIVE RISK MEASURES FOR PORTFOLIO SELECTION
      3. DISPERSION MEASURES
      4. SAFETY-FIRST RISK MEASURES
      5. KEY POINTS
      6. NOTES
    6. Back-Testing Market Risk Models
      1. STATISTICAL BACK-TESTING
      2. EXCEEDANCE-BASED STATISTICAL APPROACHES
      3. STATISTICAL BACK-TESTING OF VaRs AT MULTIPLE CONFIDENCE LEVELS
      4. USING BACK-TESTS FOR DIAGNOSTIC PURPOSES
      5. RANKING ALTERNATIVE MODELS
      6. KEY POINTS
    7. Estimating Liquidity Risks
      1. LIQUIDITY AND LIQUIDITY RISKS
      2. ESTIMATING LIQUIDITY-ADJUSTED VaR
      3. ESTIMATING LIQUIDITY-AT-RISK (LAR)
      4. ESTIMATING LIQUIDITY IN CRISES
      5. KEY POINTS
    8. Estimate of Downside Risk with Fat-Tailed and Skewed Models
      1. DOWNSIDE RISK MEASURE
      2. LÉVY STABLE DISTRIBUTION
      3. STUDENT'S t-DISTRIBUTION
      4. MIXTURE OF NORMAL DISTRIBUTIONS
      5. MODELING RETURN DISTRIBUTIONS FOR MAJOR INDEXES
      6. KEY POINTS
      7. NOTE
    9. Moving Average Models for Volatility and Correlation, and Covariance Matrices
      1. BASIC PROPERTIES OF COVARIANCE AND CORRELATION MATRICES
      2. EQUALLY WEIGHTED AVERAGES
      3. EXPONENTIALLY WEIGHTED MOVING AVERAGES
      4. KEY POINTS
  13. Software for Financial Modeling
    1. Introduction to Financial Model Building with MATLAB
      1. THE MATLAB DESKTOP AND EDITOR
      2. BASIC OPERATIONS AND MATRIX ARRAY CONSTRUCTION
      3. IMPORTANT MATLAB FUNCTIONS
      4. CREATING USER-DEFINED FUNCTIONS
      5. CONTROL FLOW STATEMENTS
      6. GRAPHS
      7. IMPORTING DATA AND INTERACTING WITH SPREADSHEETS
      8. EXAMPLES
      9. KEY POINTS
    2. Introduction to Visual Basic for Applications
      1. A SIMPLE EXAMPLE OF A VBA PROGRAM
      2. OBJECTS, PROPERTIES, AND METHODS
      3. PROGRAMMING TIPS
      4. DEBUGGING
      5. EXAMPLES
      6. KEY POINTS
      7. NOTE
  14. Stochastic Processes and Tools
    1. Stochastic Integrals
      1. THE INTUITION BEHIND STOCHASTIC INTEGRALS
      2. BROWNIAN MOTION DEFINED
      3. PROPERTIES OF BROWNIAN MOTION
      4. STOCHASTIC INTEGRALS DEFINED
      5. SOME PROPERTIES OF ITO STOCHASTIC INTEGRALS
      6. KEY POINTS
      7. NOTES
    2. Stochastic Differential Equations
      1. THE INTUITION BEHIND STOCHASTIC DIFFERENTIAL EQUATIONS
      2. ITÔ PROCESSES
      3. THE ONE-DIMENSIONAL ITÔ FORMULA
      4. STOCHASTIC DIFFERENTIAL EQUATIONS
      5. GENERALIZATION TO SEVERAL DIMENSIONS
      6. SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS
      7. KEY POINTS
      8. NOTE
    3. Stochastic Processes in Continuous Time
      1. SOME PRELIMINARIES
      2. POISSON PROCESS
      3. PURE JUMP PROCESS
      4. BROWNIAN MOTION
      5. TIME-CHANGED BROWNIAN MOTION
      6. LéVY PROCESS
      7. KEY POINTS
    4. Conditional Expectation and Change of Measure
      1. EVENTS, σ-FIELDS, AND FILTRATION
      2. CONDITIONAL EXPECTATION
      3. CHANGE OF MEASURES
      4. KEY POINTS
      5. NOTES
    5. Change of Time Methods
      1. CHANGE OF TIME METHOD
      2. APPLICATIONS OF CHANGE OF TIME METHOD
      3. KEY POINTS
      4. NOTES
  15. Term Structure Modeling
    1. The Concept and Measures of Interest Rate Volatility
      1. BASIC DEFINITIONS AND FIRST FINDINGS
      2. A DIFFUSIVE MODEL FOR RANDOMNESS
      3. MEAN REVERSION AND MARKET STABILITY
      4. THE RATE DISTRIBUTION
      5. INTEREST RATE JUMPS
      6. KEY POINTS
      7. ACKNOWLEDGMENTS
    2. Short-Rate Term Structure Models
      1. THE CONCEPT OF SHORT-RATE MODELING
      2. SINGLE-FACTOR SHORT-RATE MODELS
      3. WHICH MODEL IS BETTER?
      4. ADDING A SECOND FACTOR TO SHORT-RATE MODELS
      5. THE CONCEPT OF AFFINE MODELING
      6. KEY POINTS
      7. ACKNOWLEDGMENTS
    3. Static Term Structure Modeling in Discrete and Continuous Time
      1. INTRODUCTION TO TERM STRUCTURE MODELING
      2. TERM STRUCTURE MODELS
      3. DISCRETE-TIME MODELS OF THE TERM STRUCTURE
      4. DISCOUNT FUNCTION
      5. SPOT YIELD CURVE
      6. IMPLIED FORWARD RATE
      7. TERM STRUCTURE IN A CERTAIN ECONOMY
      8. TERM STRUCTURE IN THE REAL WORLD—NOTHING IS CERTAIN
      9. CONTINUOUS-TIME MODELS OF THE TERM STRUCTURE
      10. DISCOUNT FUNCTION
      11. FORWARD RATE
      12. TERM STRUCTURE IN CONTINUOUS TIME
      13. KEY POINTS
    4. The Dynamic Term Structure Model
      1. KEY ELEMENTS IN A DYNAMIC TERM STRUCTURE MODEL
      2. EQUILIBRIUM
      3. ARBITRAGE-FREE
      4. CONTINUOUS TIME/CONTINUOUS STATE
      5. COMPLETENESS OF MARKETS
      6. DYNAMIC TERM STRUCTURE MODEL
      7. SPOT-RATE MODEL
      8. BOND-PRICE VALUATION MODEL
      9. THE TERM STRUCTURE
      10. APPLICATIONS OF THE TERM STRUCTURE MODEL
      11. TERM STRUCTURE OF FORWARD RATES
      12. HEATH, JARROW, AND MORTON MODEL OF THE TERM STRUCTURE
      13. MARKET PRICE OF RISK
      14. BOND PRICING
      15. CHANGE OF NUMERAIRE
      16. MARKET MODELS
      17. INTEREST RATE DERIVATIVES
      18. DESIGNING YOUR NEXT MODEL
      19. KEY POINTS
    5. Essential Classes of Interest Rate Models and Their Use
      1. CATEGORIZATION OF APPROACHES TO TERM STRUCTURE MODELING
      2. WHEN DO I USE EACH OF THE MODELING APPROACHES?
      3. USING MODELS OF BORROWER BEHAVIOR WITH A RISK-NEUTRAL INTEREST RATE MODEL
      4. KEY POINTS
      5. NOTES
    6. A Review of No Arbitrage Interest Rate Models
      1. THE GENERAL MODELS FOR THE SHORT RATE
      2. BINOMIAL AND TRINOMIAL SOLUTIONS TO THE STOCHASTIC DIFFERENTIAL EQUATIONS
      3. COMPARATIVE STUDY OF THE NUMERICAL SOLUTIONS
      4. APPENDIX
      5. KEY POINTS
      6. NOTES
  16. Trading Cost Models
    1. Modeling Market Impact Costs
      1. MARKET IMPACT COSTS
      2. LIQUIDITY AND TRANSACTION COSTS
      3. MARKET IMPACT MEASUREMENTS AND EMPIRICAL FINDINGS
      4. FORECASTING AND MODELING MARKET IMPACT
      5. KEY POINTS
      6. NOTES
  17. Volatility
    1. Monte Carlo Simulation in Finance
      1. MAIN IDEAS AND IMPORTANT CONCEPTS
      2. FINANCIAL APPLICATIONS OF SIMULATION
      3. RANDOM NUMBER GENERATION
      4. VARIANCE REDUCTION TECHNIQUES
      5. SIMULATION SOFTWARE
      6. KEY POINTS
      7. NOTES
    2. Stochastic Volatility
      1. NONSTOCHASTIC VOLATILITY MEASURES
      2. KEY POINTS
      3. NOTES
  18. Index