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Financial Modeling Principles
by Frank J. Fabozzi
Encyclopedia of Financial Models, 3 Volume Set
Volume 1
Title Page
Copyright
About the Editor
Contributors
Preface
TOPIC CATEGORIES
Guide to the Encyclopedia of Financial Models
ORGANIZATION
Asset Allocation
Mean-Variance Model for Portfolio Selection
SOME BASIC CONCEPTS
MEASURING A PORTFOLIO’S EXPECTED RETURN
MEASURING PORTFOLIO RISK
PORTFOLIO DIVERSIFICATION
CHOOSING A PORTFOLIO OF RISKY ASSETS
ROBUST PORTFOLIO OPTIMIZATION
KEY POINTS
NOTES
REFERENCES
Principles of Optimization for Portfolio Selection
UNCONSTRAINED OPTIMIZATION
CONSTRAINED OPTIMIZATION
KEY POINTS
REFERENCES
Asset Allocation and Portfolio Construction Techniques in Designing the Performance-Seeking Portfolio
THE TANGENCY PORTFOLIO AS THE RATIONALE BEHIND SHARPE RATIO MAXIMIZATION
ROBUST ESTIMATORS FOR COVARIANCE PARAMETERS
ROBUST ESTIMATORS FOR EXPECTED RETURNS
IMPLICATIONS FOR BENCHMARK PORTFOLIO CONSTRUCTION
ASSET ALLOCATION MODELING: PUTTING THE EFFICIENT BUILDING BLOCKS TOGETHER
KEY POINTS
NOTES
REFERENCES
Asset Pricing Models
General Principles of Asset Pricing
ONE-PERIOD FINITE STATE ECONOMY
PORTFOLIOS AND MARKET COMPLETENESS
THE LAW OF ONE PRICE AND LINEAR PRICING
ARBITRAGE AND POSITIVE STATE PRICING
THE FUNDAMENTAL THEOREM OF ASSET PRICING
DISCOUNT FACTOR MODELS
STOCHASTIC DISCOUNT FACTORS
KEY POINTS
REFERENCES
Capital Asset Pricing Models
INTRODUCTION
SHARPE-LINTNER CAPM
ROY CAPM
CONFUSIONS REGARDING THE CAPM
TWO MEANINGS OF MARKET EFFICIENCY
CAPM INVESTORS DO NOT GET PAID FOR BEARING RISK
THE “TWO BETA” TRAP
KEY POINTS
NOTES
REFERENCES
Modeling Asset Price Dynamics
FINANCIAL TIME SERIES
BINOMIAL TREES
ARITHMETIC RANDOM WALKS
GEOMETRIC RANDOM WALKS
MEAN REVERSION
ADVANCED RANDOM WALK MODELS
STOCHASTIC PROCESSES
KEY POINTS
REFERENCES
Arbitrage Pricing: Finite-State Models
THE ARBITRAGE PRINCIPLE
ARBITRAGE PRICING IN A ONE-PERIOD SETTING
ARBITRAGE PRICING IN A MULTIPERIOD FINITE-STATE SETTING
THE BINOMIAL MODEL
ARBITRAGE PRICING IN A DISCRETE-TIME, CONTINUOUS-STATE SETTING
KEY POINTS
NOTES
REFERENCES
Arbitrage Pricing: Continuous-State, Continuous-Time Models
THE ARBITRAGE PRINCIPLE IN CONTINUOUS TIME
ARBITRAGE PRICING IN CONTINUOUS-STATE, CONTINUOUS-TIME
OPTION PRICING
STATE-PRICE DEFLATORS
EQUIVALENT MARTINGALE MEASURES
EQUIVALENT MARTINGALE MEASURES AND GIRSANOV'S THEOREM
EQUIVALENT MARTINGALE MEASURES AND COMPLETE MARKETS
EQUIVALENT MARTINGALE MEASURES AND STATE PRICES
ARBITRAGE PRICING WITH A PAYOFF RATE
IMPLICATIONS OF THE ABSENCE OF ARBITRAGE
WORKING WITH EQUIVALENT MARTINGALE MEASURES
KEY POINTS
NOTES
REFERENCES
Bayesian Analysis and Financial Modeling Applications
Basic Principles of Bayesian Analysis
THE LIKELIHOOD FUNCTION
BAYES’ THEOREM
KEY POINTS
NOTES
REFERENCES
Introduction to Bayesian Inference
PRIOR INFORMATION
POSTERIOR INFERENCE
BAYESIAN PREDICTIVE INFERENCE
ILLUSTRATION: POSTERIOR TRADE-OFF AND THE NORMAL MEAN PARAMETER
KEY POINTS
NOTES
REFERENCES
Bayesian Linear Regression Model
THE UNIVARIATE LINEAR REGRESSION MODEL
THE MULTIVARIATE LINEAR REGRESSION MODEL
KEY POINTS
NOTES
REFERENCES
Bayesian Estimation of ARCH-Type Volatility Models
BAYESIAN ESTIMATION OF THE GARCH(1,1) MODEL
MARKOV-SWITCHING GARCH MODELS
APPENDIX: THE GRIDDY GIBBS SAMPLER
KEY POINTS
NOTES
REFERENCES
Bayesian Techniques and the Black-Litterman Model
PRACTICAL PROBLEMS ENCOUNTERED IN MEAN-VARIANCE OPTIMIZATION
SHRINKAGE ESTIMATION
THE BLACK-LITTERMAN MODEL
KEY POINTS
NOTES
REFERENCES
Bond Valuation
Basics of Bond Valuation
GENERAL PRINCIPLES OF BOND VALUATION
ARBITRAGE-FREE BOND VALUATION
KEY POINTS
NOTES
REFERENCES
Relative Value Analysis of Fixed-Income Products
YIELD SPREADS OVER SWAP AND TREASURY CURVES
ASSET SWAPS
CREDIT DEFAULT SWAPS
KEY POINTS
NOTES
REFERENCES
Yield Curves and Valuation Lattices
THE INTEREST RATE LATTICE
CALIBRATING THE LATTICE
USING THE LATTICE FOR VALUATION
KEY POINTS
NOTE
REFERENCES
Using the Lattice Model to Value Bonds with Embedded Options, Floaters, Options, and Caps/Floors
FIXED-COUPON BONDS WITH EMBEDDED OPTIONS
FLOATING-COUPON BONDS WITH EMBEDDED OPTIONS
VALUING CAPS AND FLOORS
VALUATION OF TWO MORE EXOTIC STRUCTURES
VALUING AN OPTION ON A BOND
EXTENSIONS
KEY POINTS
NOTES
REFERENCES
Understanding the Building Blocks for OAS Models
IS IT EQUILIBRIUM OR AN ARBITRAGE MODEL?
WHICH IS THE RIGHT MODEL OF THE INTEREST RATE PROCESS?
TERM STRUCTURE MODELS: WHICH IS THE RIGHT APPROACH FOR OAS?
IS THERE A RIGHT WAY TO MODEL PREPAYMENTS?
KEY POINTS
NOTES
REFERENCES
Quantitative Models to Value Convertible Bonds
ANALYTICAL MODELS
NUMERICAL MODELS
KEY POINTS
REFERENCES
Quantitative Approaches to Inflation-Indexed Bonds
BOND STRUCTURES AND THE CONCEPT OF REAL YIELD
INFLATION-INDEXED BONDS IN A NOMINAL PORTFOLIO
ADVANCED ANALYTICAL APPROACHES TO INFLATION-INDEXED BONDS
KEY POINTS
NOTES
REFERENCES
Credit Risk Modeling
An Introduction to Credit Risk Models
KEY OBJECTIVES IN CREDIT RISK MODELING
RATINGS AND “CREDIT SCORES” VERSUS DEFAULT PROBABILITIES
WHAT “THROUGH THE CYCLE” REALLY MEANS
VALUATION, PRICING, AND HEDGING
EMPIRICAL DATA ON CREDIT SPREADS AND COMMON STOCK PRICES
STRUCTURAL MODELS OF RISKY DEBT
REDUCED-FORM MODELS OF RISKY DEBT
EMPIRICAL EVIDENCE ON MODEL PERFORMANCE
KEY POINTS
NOTES
REFERENCES
Default Correlation in Intensity Models for Credit Risk Modeling
PRELIMINARIES
SINGLE ENTITY
DEFAULT CORRELATION
KEY POINTS
NOTES
REFERENCES
Structural Models in Credit Risk Modeling
REVIEW OF STRUCTURAL MODELS
SINGLE FIRM
DEFAULT CORRELATION
KEY POINTS
NOTES
REFERENCES
Modeling Portfolio Credit Risk
ELEMENTS OF CREDIT RISK
KEY POINTS
REFERENCES
Simulating the Credit Loss Distribution
MONTE CARLO METHODS
KEY POINTS
REFERENCES
Managing Credit Spread Risk Using Duration Times Spread (DTS)
THE DTS CONCEPT
DTS AS BETA-ADJUSTED SPREAD DURATION
THE RELATION BETWEEN SPREAD VOLATILITY AND SPREAD LEVEL
DTS AND EXCESS RETURN VOLATILITY
IMPLICATIONS OF DTS FOR PORTFOLIO MANAGERS
KEY POINTS
NOTES
REFERENCES
Credit Spread Decomposition
REVEALING THE DRIVERS OF CREDIT SPREADS
CREDIT SPREAD DECOMPOSITION: MODEL SPECIFICATION AND IMPLEMENTATION
INTERPRETING THE RESULTS OF THE CREDIT SPREAD DECOMPOSITION MODEL
APPLICATIONS OF CREDIT SPREAD DECOMPOSITION
ALTERNATIVE CREDIT SPREAD DECOMPOSITION MODELS
KEY POINTS
NOTES
REFERENCES
Credit Derivatives and Hedging Credit Risk
CREDIT PORTFOLIO MODELING: WHAT’S THE HEDGE?
THE MERTON MODEL AND ITS VARIANTS: TRANSACTION-LEVEL HEDGING
THE MERTON MODEL AND ITS VARIANTS: PORTFOLIO- LEVEL HEDGING
CREDIT DEFAULT SWAPS AND HEDGING
PORTFOLIO- AND TRANSACTION-LEVEL HEDGING USING TRADED MACROECONOMIC INDICES
KEY POINTS
NOTES
REFERENCES
Derivatives Valuation
No-Arbitrage Price Relations for Forwards, Futures, and Swaps
UNDERSTANDING CARRY COSTS/BENEFITS
VALUING FORWARDS
VALUING FUTURES
HEDGING WITH FUTURES
SUMMARY
IMPLYING FORWARD NET CARRY RATES
VALUING SWAPS
KEY POINTS
NOTES
REFERENCES
No-Arbitrage Price Relations for Options
OPTIONS AND FORWARDS
CONTINUOUS RATES
DISCRETE FLOWS
NO-ARBITRAGE FUTURES OPTIONS RELATIONS
NO-ARBITRAGE INTERMARKET RELATIONS
KEY POINTS
NOTES
REFERENCES
Introduction to Contingent Claims Analysis
STATES OF THE WORLD
CONTINGENT CLAIMS AND THEIR VALUE
INVESTOR’S UTILITY MAXIMIZATION IN CONTINGENT CLAIMS MARKETS
INCOMPLETE MARKETS FOR CONTINGENT CLAIMS
FINANCIAL INSTRUMENTS AS CONTINGENT CLAIMS
KEY POINTS
REFERENCES
Black-Scholes Option Pricing Model
MOTIVATION
BLACK-SCHOLES FORMULA
COMPUTING A CALL OPTION PRICE
SENSITIVITY OF OPTION PRICE TO A CHANGE IN FACTORS: THE GREEKS
COMPUTING A PUT OPTION PRICE
ASSUMPTIONS UNDERLYING THE BLACK-SCHOLES MODEL AND BASIC EXTENSIONS
BLACK-SCHOLES MODEL APPLIED TO THE PRICING OF OPTIONS ON BONDS: IMPORTANCE OF ASSUMPTIONS
KEY POINTS
References
Pricing of Futures/Forwards and Options
PRICING OF FUTURES/FORWARD CONTRACTS
PRICING OF OPTIONS
KEY POINTS
REFERENCES
Pricing Options on Interest Rate Instruments
MODELING THE TERM STRUCTURE AND BOND PRICES
MODELING IN PRACTICE
HJM METHODOLOGY
BOND OPTION PRICING
PRACTICAL CONSIDERATIONS
KEY POINTS
REFERENCES
Basics of Currency Option Pricing Models
BASIC PROPERTIES
THEORETICAL VALUATION
BLACK-SCHOLES MODEL
EXAMPLES OF OTHER MODELS
PRICING WITHOUT A COMPUTER MODEL
THE PRICE OF AN OPTION
THE GREEKS
KEY POINTS
REFERENCES
Credit Default Swap Valuation
DEFAULT SWAPS
CREDIT EVENTS
PRICING CREDIT DEFAULT SWAPS BY STATIC REPLICATION
PRICING OF A SINGLE-NAME CREDIT DEFAULT SWAP
KEY POINTS
NOTES
REFERENCES
Valuation of Fixed Income Total Return Swaps
AN INTUITIVE APPROACH
USING THE DUFFIE- SINGLETON MODEL
THE FORWARD MEASURE
KEY POINTS
NOTES
REFERENCES
Pricing of Variance, Volatility, Covariance, and Correlation Swaps
DESCRIPTION OF SWAPS
MODELING AND PRICING OF VARIANCE, VOLATILITY, COVARIANCE, AND CORRELATION SWAPS WITH STOCHASTIC VOLATILITY
NUMERICAL EXAMPLE: VOLATILITY SWAP FOR S&P60 CANADA INDEX
KEY POINTS
NOTES
REFERENCES
Modeling, Pricing, and Risk Management of Assets and Derivatives in Energy and Shipping
ENERGY COMMODITY PRICE MODELS
VALUATION AND HEDGING OF DERIVATIVES
APPLICATIONS
KEY POINTS
REFERENCES
Index
Volume 2
Title Page
Copyright
About the Editor
Contributors
Preface
TOPIC CATEGORIES
Guide to the Encyclopedia of Financial Models
ORGANIZATION
Equity Models and Valuation
Dividend Discount Models
DIVIDEND MEASURES
DIVIDENDS AND STOCK PRICES
BASIC DIVIDEND DISCOUNT MODELS
THE FINITE LIFE GENERAL DIVIDEND DISCOUNT MODEL
CONSTANT GROWTH DIVIDEND DISCOUNT MODEL
MULTIPHASE DIVIDEND DISCOUNT MODELS
STOCHASTIC DIVIDEND DISCOUNT MODELS
EXPECTED RETURNS AND DIVIDEND DISCOUNT MODELS
KEY POINTS
REFERENCES
Discounted Cash Flow Methods for Equity Valuation
DIVIDEND DISCOUNT MODEL
CONSTANT-GROWTH DDM
NONCONSTANT-GROWTH DDM
INTUITION BEHIND THE DDM
COMPLICATIONS IN IMPLEMENTING THE DDM IN THE REAL WORLD
ADAPTING TO THE COMPLICATIONS: THE EARNINGS PER SHARE APPROACH
FREE CASH FLOW DCF MODEL—TOTAL FIRM VALUATION
CALCULATING FCF
USING THE CASH-FLOW STATEMENT TO ARRIVE AT OCF AND FCF
VALUING THE TOTAL FIRM
ESTIMATING TOTAL FIRM VALUE USING THE FCF MODEL
KEY POINTS
REFERENCES
Relative Valuation Methods for Equity Analysis
BASIC PRINCIPLES OF RELATIVE VALUATION
HYPOTHETICAL EXAMPLE
KEY POINTS
NOTES
REFERENCES
Equity Analysis in a Complex Market
AN INTEGRATED APPROACH TO A SEGMENTED MARKET
DISENTANGLING
CONSTRUCTING, TRADING, AND EVALUATING PORTFOLIOS
PROFITING FROM COMPLEXITY
KEY POINTS
NOTES
REFERENCES
Equity Portfolio Selection Models in Practice
PORTFOLIO CONSTRAINTS COMMONLY USED IN PRACTICE
BENCHMARK EXPOSURE AND TRACKING ERROR MINIMIZATION
INCORPORATING TRANSACTION COSTS
INCORPORATING TAXES
MULTIACCOUNT OPTIMIZATION
ROBUST PARAMETER ESTIMATION
PORTFOLIO RESAMPLING
ROBUST PORTFOLIO OPTIMIZATION
KEY POINTS
NOTES
REFERENCES
Basics of Quantitative Equity Investing
EQUITY INVESTING
FUNDAMENTAL VS. QUANTITATIVE INVESTOR
THE QUANTITATIVE STOCK SELECTION MODEL
THE OVERALL QUANTITATIVE INVESTMENT PROCESS
RESEARCH
PORTFOLIO CONSTRUCTION
MONITORING
CURRENT TRENDS
KEY POINTS
NOTES
Quantitative Equity Portfolio Management
TRADITIONAL AND QUANTITATIVE APPROACHES TO EQUITY PORTFOLIO MANAGEMENT
FORECASTING STOCK RETURNS, RISKS, AND TRANSACTION COSTS
CONSTRUCTING PORTFOLIOS
TRADING
EVALUATING RESULTS AND UPDATING THE PROCESS
KEY POINTS
REFERENCES
Forecasting Stock Returns
THE CONCEPT OF PREDICTABILITY
A CLOSER LOOK AT PRICING MODELS
PREDICTIVE RETURN MODELS
IS FORECASTING MARKETS WORTH THE EFFORT?
KEY POINTS
NOTES
REFERENCES
Factor Models for Portfolio Construction
Factor Models
ARBITRAGE PRICING THEORY
TYPES OF FACTOR MODELS
FACTOR MODEL ESTIMATION
USE OF PRINCIPAL COMPONENTS ANALYSIS
KEY POINTS
REFERENCES
Principal Components Analysis and Factor Analysis
FACTOR MODELS
PRINCIPAL COMPONENTS ANALYSIS
FACTOR ANALYSIS
PCA AND FACTOR ANALYSIS COMPARED
KEY POINTS
REFERENCES
Multifactor Equity Risk Models and Their Applications
MOTIVATION
EQUITY RISK FACTOR MODELS
APPLICATIONS OF EQUITY RISK MODELS
KEY POINTS
NOTES
REFERENCES
Factor-Based Equity Portfolio Construction and Analysis
FACTOR-BASED TRADING
DEVELOPING FACTOR-BASED TRADING STRATEGIES
RISK TO TRADING STRATEGIES
DESIRABLE PROPERTIES OF FACTORS
SOURCES FOR FACTORS
BUILDING FACTORS FROM COMPANY CHARACTERISTICS
WORKING WITH DATA
ANALYSIS OF FACTOR DATA
KEY POINTS
NOTES
REFERENCES
Cross-Sectional Factor-Based Models and Trading Strategies
CROSS-SECTIONAL METHODS FOR EVALUATION OF FACTOR PREMIUMS
FACTOR MODELS
PERFORMANCE EVALUATION OF FACTORS
MODEL CONSTRUCTION METHODOLOGIES FOR A FACTOR-BASED TRADING STRATEGY
BACKTESTING
BACKTESTING OUR FACTOR TRADING STRATEGY
KEY POINTS
APPENDIX: THE COMPUSTAT POINT-IN-TIME, IBES CONSENSUS DATABASES AND FACTOR DEFINITIONS
NOTES
REFERENCES
The Fundamentals of Fundamental Factor Models
FUNDAMENTAL ANALYSIS AND THE BARRA FUNDAMENTAL FACTOR MODEL
CRITICAL INSIGHTS FROM THE BARRA FUNDAMENTAL FACTOR MODEL
RISK DECOMPOSITION
KEY POINTS
NOTES
REFERENCES
Multifactor Equity Risk Models and Their Applications
MODEL DESCRIPTION AND ESTIMATION
RISK DECOMPOSITION
APPLICATIONS IN PORTFOLIO CONSTRUCTION AND RISK CONTROL
KEY POINTS
NOTES
REFERENCES
Multifactor Fixed Income Risk Models and Their Applications
APPROACHES USED TO ANALYZE RISK
APPLICATIONS OF RISK MODELING
KEY POINTS
NOTES
REFERENCES
Financial Econometrics
Scope and Methods of Financial Econometrics
THE DATA GENERATING PROCESS
FINANCIAL ECONOMETRICS AT WORK
TIME HORIZON OF MODELS
APPLICATIONS
KEY POINTS
REFERENCES
Regression Analysis: Theory and Estimation
THE CONCEPT OF DEPENDENCE
REGRESSIONS AND LINEAR MODELS
ESTIMATION OF LINEAR REGRESSIONS
SAMPLING DISTRIBUTIONS OF REGRESSIONS
DETERMINING THE EXPLANATORY POWER OF A REGRESSION
USING REGRESSION ANALYSIS IN FINANCE
NONNORMALITY AND AUTOCORRELATION OF THE RESIDUALS
PITFALLS OF REGRESSIONS
KEY POINTS
NOTES
REFERENCES
Categorical and Dummy Variables in Regression Models
INDEPENDENT CATEGORICAL VARIABLES
DEPENDENT CATEGORICAL VARIABLES
KEY POINTS
NOTE
REFERENCES
Quantile Regression
COMPARING QUANTILE AND OLS APPROACHES
REASONS FOR USING QUANTILE METHODS
BACKGROUND AND FURTHER EXAMPLES
KEY POINTS
REFERENCES
ARCH/GARCH Models in Applied Financial Econometrics
REVIEW OF LINEAR REGRESSION AND AUTOREGRESSIVE MODELS
ARCH/GARCH MODELS
WHY ARCH/GARCH?
GENERALIZATIONS OF THE ARCH/GARCH MODELS
KEY POINTS
REFERENCES
Classification and Regression Trees and Their Use in Financial Modeling
TECHNICAL DETAILS
TREE PRUNING
STRENGTHS AND WEAKNESSES OF CART
APPLICATION OF CART IN STOCK SELECTION
KEY POINTS
NOTE
ACKNOWLEDGMENT
REFERENCES
Applying Cointegration to Problems in Finance
STATIONARY AND NONSTATIONARY VARIABLES AND COINTEGRATION
TESTING FOR COINTEGRATION
KEY POINTS
NOTES
REFERENCES
Nonlinearity and Nonlinear Econometric Models in Finance
STUDY OF NONLINEARITY IN ECONOMETRICS AND STATISTICS
NONLINEAR MODELS
NONLINEARITY TESTS
1 MODELING
FORECASTING
2 APPLICATION
KEY POINTS
REFERENCES
Robust Estimates of Betas and Correlations
OLS REVISITED
THEIL-SEN REGRESSION
ROBUST ESTIMATES OF BETA
ROBUST ESTIMATES OF CORRELATION
KEY POINTS
REFERENCES
Working with High-Frequency Data
WHAT ARE HIGH-FREQUENCY DATA?
HOW ARE HIGH-FREQUENCY DATA RECORDED?
PROPERTIES OF HIGH-FREQUENCY DATA
HIGH-FREQUENCY DATA ARE VOLUMINOUS
HIGH-FREQUENCY DATA ARE SUBJECT TO BID-ASK BOUNCE
HIGH-FREQUENCY DATA ARE IRREGULARLY SPACED IN TIME
KEY POINTS
REFERENCES
Financial Modeling Principles
Milestones in Financial Modeling
THE PRECURSORS: PARETO, WALRAS, AND THE LAUSANNE SCHOOL
PRICE DIFFUSION: BACHELIER
THE RUIN PROBLEM IN INSURANCE: LUNDBERG
THE PRINCIPLES OF INVESTMENT: MARKOWITZ
UNDERSTANDING VALUE: MODIGLIANI AND MILLER
EFFICIENT MARKETS: FAMA AND SAMUELSON
CAPITAL ASSET PRICING MODEL: SHARPE, LINTNER, AND MOSSIN
THE MULTIFACTOR CAPM: MERTON
ARBITRAGE PRICING THEORY: ROSS
ARBITRAGE, HEDGING, AND OPTION THEORY: BLACK, SCHOLES, AND MERTON
KEY POINTS
REFERENCES
From Art to Financial Modeling
THE ROLE OF INFORMATION TECHNOLOGY
INTEGRATING QUALITATIVE AND QUANTITATIVE INFORMATION
PRINCIPLES FOR ENGINEERING A SUITE OF MODELS
KEY POINTS
REFERENCES
Basic Data Description for Financial Modeling and Analysis
DATA TYPES
FREQUENCY DISTRIBUTIONS
EMPIRICAL CUMULATIVE FREQUENCY DISTRIBUTION
DATA CLASSES
CUMULATIVE FREQUENCY DISTRIBUTIONS
KEY POINTS
NOTES
REFERENCES
Time Series Concepts, Representations, and Models
CONCEPTS OF TIME SERIES
STYLIZED FACTS OF FINANCIAL TIME SERIES
INFINITE MOVING-AVERAGE AND AUTOREGRESSIVE REPRESENTATION OF TIME SERIES
ARMA REPRESENTATIONS
INTEGRATED SERIES AND TRENDS
APPENDIX
KEY POINTS
NOTE
REFERENCES
Extracting Risk-Neutral Density Information from Options Market Prices
AN APPROPRIATE PARAMETRIC MODEL
TWO PARAMETRIC MODELS FOR RND ESTIMATION
FITTING THE MODELS TO DATA
KEY POINTS
NOTE
REFERENCES
Financial Statement Analysis
Financial Statements
ACCOUNTING PRINCIPLES
INFORMATION CONVEYED BY THE BASIC FINANCIAL STATEMENTS
ACCOUNTING FLEXIBILITY
KEY POINTS
NOTES
REFERENCES
Financial Ratio Analysis
RATIOS AND THEIR CLASSIFICATION
RETURN-ON-INVESTMENT RATIOS
LIQUIDITY
PROFITABILITY RATIOS
ACTIVITY RATIOS
FINANCIAL LEVERAGE RATIOS
COMMON-SIZE ANALYSIS
USING FINANCIAL RATIO ANALYSIS
KEY POINTS
REFERENCES
Cash-Flow Analysis
DIFFICULTIES WITH MEASURING CASH FLOW
CASH FLOWS AND THE STATEMENT OF CASH FLOWS
FREE CASH FLOW
CALCULATING FREE CASH FLOW
NET FREE CASH FLOW
USEFULNESS OF CASH FLOWS IN FINANCIAL ANALYSIS
KEY POINTS
REFERENCES
Finite Mathematics for Financial Modeling
Important Functions and Their Features
CONTINUOUS FUNCTION
INDICATOR FUNCTION
DERIVATIVES
MONOTONIC FUNCTION
INTEGRAL
SOME FUNCTIONS
KEY POINTS
REFERENCES
Time Value of Money
IMPORTANCE OF THE TIME VALUE OF MONEY
DETERMINING THE FUTURE VALUE
DETERMINING THE PRESENT VALUE
DETERMINING THE UNKNOWN INTEREST RATE
DETERMINING THE NUMBER OF COMPOUNDING PERIODS
THE TIME VALUE OF A SERIES OF CASH FLOWS
VALUING CASH FLOWS WITH DIFFERENT TIME PATTERNS
LOAN AMORTIZATION
THE CALCULATION OF INTEREST RATES AND YIELDS
KEY POINTS
NOTE
REFERENCES
Fundamentals of Matrix Algebra
VECTORS AND MATRICES DEFINED
SQUARE MATRICES
DETERMINANTS
SYSTEMS OF LINEAR EQUATIONS
LINEAR INDEPENDENCE AND RANK
VECTOR AND MATRIX OPERATIONS
MATRIX OPERATIONS
EIGENVALUES AND EIGENVECTORS
KEY POINTS
NOTES
Difference Equations
THE LAG OPERATOR L
HOMOGENEOUS DIFFERENCE EQUATIONS
NONHOMOGENEOUS DIFFERENCE EQUATIONS
SYSTEMS OF LINEAR DIFFERENCE EQUATIONS
SYSTEMS OF HOMOGENEOUS LINEAR DIFFERENCE EQUATIONS
KEY POINTS
NOTE
REFERENCES
Differential Equations
DIFFERENTIAL EQUATIONS DEFINED
ORDINARY DIFFERENTIAL EQUATIONS
SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
CLOSED-FORM SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
NONLINEAR DYNAMICS AND CHAOS
KEY POINTS
NOTES
REFERENCES
Partial Differential Equations in Finance
PARTIAL DIFFERENTIAL EQUATIONS FOR OPTION PRICING
PRICING EUROPEAN OPTIONS WITH PDES
PRICING AMERICAN OPTIONS WITH PDES
CALIBRATION
KEY POINTS
NOTES
REFERENCES
Model Risk and Selection
Model Risk
MODELS AND MODEL RISK
SOURCES OF MODEL RISK
MANAGING MODEL RISK
KEY POINTS
REFERENCES
Model Selection and Its Pitfalls
MODEL SELECTION AND ESTIMATION
THE (MACHINE) LEARNING APPROACH TO MODEL SELECTION
SAMPLE SIZE AND MODEL COMPLEXITY
DANGEROUS PATTERNS OF BEHAVIOR
DATA SNOOPING
SURVIVORSHIP BIASES AND OTHER SAMPLE DEFECTS
MOVING TRAINING WINDOWS
MODEL RISK
MODEL SELECTION IN A NUTSHELL
KEY POINTS
REFERENCES
Managing the Model Risk with the Methods of the Probabilistic Decision Theory
AN OUTLINE OF PROBABLISTIC DECISION THEORY
MODEL RISK OF A SIMPLE PORTFOLIO
INVESTMENT IN A RISKY BOND
KEY POINTS
REFERENCES
Fat-Tailed Models for Risk Estimation
THE FUNDAMENTALS: NORMAL DISTRIBUTION
INCORPORATING HEAVY TAILS AND SKEWNESS: PARAMETRIC FAT-TAILED MODELS
INCORPORATING HEAVY TAILS AND SKEWNESS: SEMI-PARAMETRIC FAT-TAILED MODELS
COMPARISON AMONG RISK MODELS
KEY POINTS
NOTES
REFERENCES
Index
Volume 3
Title Page
Copyright
About the Editor
Contributors
Preface
TOPIC CATEGORIES
Guide to the Encyclopedia of Financial Models
Organization
Mortgage-Backed Securities Analysis and Valuation
Valuing Mortgage-Backed and Asset-Backed Securities
CASH-FLOW YIELD ANALYSIS
ZERO-VOLATILITY SPREAD
VALUATION USING MONTE CARLO SIMULATION AND OAS ANALYSIS
MEASURING INTEREST RISK
KEY POINTS
NOTES
The Active-Passive Decomposition Model for MBS
PATH-DEPENDENCE AND PRICING PARTIAL DIFFERENTIAL EQUATION
EXTENDED ACTIVE-PASSIVE DECOMPOSITION MODEL
EXTENSIONS AND NUANCES
KEY POINTS
NOTES
Analysis of Nonagency Mortgage-Backed Securities
FACTORS IMPACTING RETURNS FROM NONAGENCY MBS
UNDERSTANDING THE EVOLUTION OF CREDIT PERFORMANCE WITHIN A TRANSACTION
THE PROCESS OF ESTIMATING PRIVATE-LABEL MBS RETURNS
KEY POINTS
NOTES
Measurement of Prepayments for Residential Mortgage-Backed Securities
PREPAYMENT TERMINOLOGY
CALCULATING PREPAYMENT SPEEDS
DELINQUENCY, DEFAULT, AND LOSS TERMINOLOGY
KEY POINTS
NOTES
Prepayments and Factors Influencing the Return of Principal for Residential Mortgage-Backed Securities
PREPAYMENT FUNDAMENTALS
FACTORS INFLUENCING PREPAYMENT SPEEDS
DEFAULTS AND “INVOLUNTARY” PREPAYMENTS
KEY POINTS
NOTES
Operational Risk
Operational Risk
Operational Risk Defined
OPERATIONAL RISK EXPOSURE INDICATORS
CLASSIFICATION OF OPERATIONAL RISK
KEY POINTS
NOTES
Operational Risk Models
OPERATIONAL RISK MODELS
Specifics of Operational Loss Data
KEY POINTS
NOTES
Modeling Operational Loss Distributions
APPROACHES TO OPERATIONAL RISK MODELING
NONPARAMETRIC APPROACH: EMPIRICAL DISTRIBUTION FUNCTION
PARAMETRIC APPROACH: CONTINUOUS LOSS DISTRIBUTIONS
EXTENSION: MIXTURE LOSS DISTRIBUTIONS
A NOTE ON THE TAIL BEHAVIOR
EMPIRICAL EVIDENCE WITH OPERATIONAL LOSS DATA
KEY POINTS
NOTES
Optimization Tools
Introduction to Stochastic Programming and Its Applications to Finance
WHAT IS STOCHASTIC PROGRAMMING?
STOCHASTIC PROGRAMMING VERSUS OTHER METHODS IN FINANCE
A GENERAL MULTISTAGE STOCHASTIC PROGRAMMING MODEL FOR FINANCIAL PLANNING
KEY POINTS
Robust Portfolio Optimization
THE ROBUST OPTIMIZATION APPROACH
THE RELATIONSHIP TO BAYESIAN METHODS AND ECONOMIC THEORY
USING ROBUST PORTFOLIO OPTIMIZATION IN PRACTICE
PRACTICAL CONSIDERATIONS FOR ROBUST PORTFOLIO ALLOCATION
FUTURE DIRECTIONS
KEY POINTS
Probability Theory
Concepts of Probability Theory
HISTORICAL DEVELOPMENT OF ALTERNATIVE APPROACHES TO PROBABILITY
SET OPERATIONS AND PRELIMINARIES
PROBABILITY MEASURE
RANDOM VARIABLE
KEY POINTS
NOTES
Discrete Probability Distributions
DISCRETE LAW
BERNOULLI DISTRIBUTION
BINOMIAL DISTRIBUTION
HYPERGEOMETRIC DISTRIBUTION
MULTINOMIAL DISTRIBUTION
POISSON DISTRIBUTION
DISCRETE UNIFORM DISTRIBUTION
APPENDIX B Binomial and Multinomial Coefficients
BINOMIAL COEFFICIENT
MULTINOMIAL COEFFICIENT
KEY POINTS
NOTE
Continuous Probability Distributions
CONTINUOUS PROBABILITY DISTRIBUTION DESCRIBED
DISTRIBUTION FUNCTION
DENSITY FUNCTION
CONTINUOUS RANDOM VARIABLE
COMPUTING PROBABILITIES FROM THE DENSITY FUNCTION
LOCATION PARAMETERS
DISPERSION PARAMETERS
KEY POINTS
NOTES
Continuous Probability Distributions with Appealing Statistical Properties
NORMAL DISTRIBUTION
CHI-SQUARE DISTRIBUTION
STUDENT'S t-DISTRIBUTION
F-DISTRIBUTION
EXPONENTIAL DISTRIBUTION
RECTANGULAR DISTRIBUTION
GAMMA DISTRIBUTION
BETA DISTRIBUTION
LOG-NORMAL DISTRIBUTION
KEY POINTS
NOTES
Continuous Probability Distributions Dealing with Extreme Events
GENERALIZED EXTREME VALUE DISTRIBUTION
GENERALIZED PARETO DISTRIBUTION
NORMAL INVERSE GAUSSIAN DISTRIBUTION
α-STABLE DISTRIBUTION
KEY POINTS
Stable and Tempered Stable Distributions
α-STABLE DISTRIBUTION
TEMPERED STABLE DISTRIBUTIONS
INFINITELY DIVISIBLE DISTRIBUTIONS
HYPERGEOMETRIC FUNCTION AND CONFLUENT HYPERGEOMETRIC FUNCTION
KEY POINTS
NOTES
Fat Tails, Scaling, and Stable Laws
SCALING, STABLE LAWS, AND FAT TAILS
EXTREME VALUE THEORY FOR IID PROCESSES
ELIMINATING THE ASSUMPTION OF IID SEQUENCES
KEY POINTS
NOTES
Copulas
DRAWBACKS OF CORRELATION
OVERCOMING THE DRAWBACKS OF CORRELATION: COPULAS
MATHEMATICAL DEFINITION OF COPULAS
KEY POINTS
NOTES
Applications of Order Statistics to Risk Management Problems
PERFORMANCE OF VaR ESTIMATION
VaR AND DIFFERENT LEVELS OF CONFIDENCE
JOINT PROBABILITY DISTRIBUTIONS FOR ORDER STATISTICS
DISTRIBUTION-FREE CONFIDENCE INTERVALS FOR VaR
BIVARIATE ORDER STATISTICS
KEY POINTS
NOTE
Risk Measures
Measuring Interest Rate Risk: Effective Duration and Convexity
EFFECTIVE DURATION AND EFFECTIVE CONVEXITY AN EXAMPLE
PUTTING IT ALL TOGETHER
KEY POINTS
NOTES
Yield Curve Risk Measures
DURATION, CONVEXITY, AND NONPARALLEL YIELD CURVE SHIFTS
CASH-FLOW DISTRIBUTION ANALYSIS VERSUS A BENCHMARK
KEY RATE DURATION
SLOPE ELASTICITY MEASURE
YIELD CURVE RESHAPING DURATION
ANALYSIS OF LIKELY YIELD CURVE SHIFTS
KEY POINTS
NOTE
Value-at-Risk
VALUE-AT-RISK DEFINED
COMPUTING PORTFOLIO VaR IN PRACTICE
BACK-TESTING OF VaR
COHERENT RISK MEASURES
KEY POINTS
NOTES
Average Value-at-Risk
AVERAGE VALUE-AT-RISK DEFINED
AVaR ESTIMATION FROM A SAMPLE
COMPUTING PORTFOLIO AVAR IN PRACTICE
BACK-TESTING OF AVaR
TECHNICAL APPENDIX
KEY POINTS
NOTES
Risk Measures and Portfolio Selection
DESIRABLE FEATURES OF INVESTMENT RISK MEASURES
ALTERNATIVE RISK MEASURES FOR PORTFOLIO SELECTION
DISPERSION MEASURES
SAFETY-FIRST RISK MEASURES
KEY POINTS
NOTES
Back-Testing Market Risk Models
STATISTICAL BACK-TESTING
EXCEEDANCE-BASED STATISTICAL APPROACHES
STATISTICAL BACK-TESTING OF VaRs AT MULTIPLE CONFIDENCE LEVELS
USING BACK-TESTS FOR DIAGNOSTIC PURPOSES
RANKING ALTERNATIVE MODELS
KEY POINTS
Estimating Liquidity Risks
LIQUIDITY AND LIQUIDITY RISKS
ESTIMATING LIQUIDITY-ADJUSTED VaR
ESTIMATING LIQUIDITY-AT-RISK (LAR)
ESTIMATING LIQUIDITY IN CRISES
KEY POINTS
Estimate of Downside Risk with Fat-Tailed and Skewed Models
DOWNSIDE RISK MEASURE
LÉVY STABLE DISTRIBUTION
STUDENT'S t-DISTRIBUTION
MIXTURE OF NORMAL DISTRIBUTIONS
MODELING RETURN DISTRIBUTIONS FOR MAJOR INDEXES
KEY POINTS
NOTE
Moving Average Models for Volatility and Correlation, and Covariance Matrices
BASIC PROPERTIES OF COVARIANCE AND CORRELATION MATRICES
EQUALLY WEIGHTED AVERAGES
EXPONENTIALLY WEIGHTED MOVING AVERAGES
KEY POINTS
Software for Financial Modeling
Introduction to Financial Model Building with MATLAB
THE MATLAB DESKTOP AND EDITOR
BASIC OPERATIONS AND MATRIX ARRAY CONSTRUCTION
IMPORTANT MATLAB FUNCTIONS
CREATING USER-DEFINED FUNCTIONS
CONTROL FLOW STATEMENTS
GRAPHS
IMPORTING DATA AND INTERACTING WITH SPREADSHEETS
EXAMPLES
KEY POINTS
Introduction to Visual Basic for Applications
A SIMPLE EXAMPLE OF A VBA PROGRAM
OBJECTS, PROPERTIES, AND METHODS
PROGRAMMING TIPS
DEBUGGING
EXAMPLES
KEY POINTS
NOTE
Stochastic Processes and Tools
Stochastic Integrals
THE INTUITION BEHIND STOCHASTIC INTEGRALS
BROWNIAN MOTION DEFINED
PROPERTIES OF BROWNIAN MOTION
STOCHASTIC INTEGRALS DEFINED
SOME PROPERTIES OF ITO STOCHASTIC INTEGRALS
KEY POINTS
NOTES
Stochastic Differential Equations
THE INTUITION BEHIND STOCHASTIC DIFFERENTIAL EQUATIONS
ITÔ PROCESSES
THE ONE-DIMENSIONAL ITÔ FORMULA
STOCHASTIC DIFFERENTIAL EQUATIONS
GENERALIZATION TO SEVERAL DIMENSIONS
SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS
KEY POINTS
NOTE
Stochastic Processes in Continuous Time
SOME PRELIMINARIES
POISSON PROCESS
PURE JUMP PROCESS
BROWNIAN MOTION
TIME-CHANGED BROWNIAN MOTION
LéVY PROCESS
KEY POINTS
Conditional Expectation and Change of Measure
EVENTS, σ-FIELDS, AND FILTRATION
CONDITIONAL EXPECTATION
CHANGE OF MEASURES
KEY POINTS
NOTES
Change of Time Methods
CHANGE OF TIME METHOD
APPLICATIONS OF CHANGE OF TIME METHOD
KEY POINTS
NOTES
Term Structure Modeling
The Concept and Measures of Interest Rate Volatility
BASIC DEFINITIONS AND FIRST FINDINGS
A DIFFUSIVE MODEL FOR RANDOMNESS
MEAN REVERSION AND MARKET STABILITY
THE RATE DISTRIBUTION
INTEREST RATE JUMPS
KEY POINTS
ACKNOWLEDGMENTS
Short-Rate Term Structure Models
THE CONCEPT OF SHORT-RATE MODELING
SINGLE-FACTOR SHORT-RATE MODELS
WHICH MODEL IS BETTER?
ADDING A SECOND FACTOR TO SHORT-RATE MODELS
THE CONCEPT OF AFFINE MODELING
KEY POINTS
ACKNOWLEDGMENTS
Static Term Structure Modeling in Discrete and Continuous Time
INTRODUCTION TO TERM STRUCTURE MODELING
TERM STRUCTURE MODELS
DISCRETE-TIME MODELS OF THE TERM STRUCTURE
DISCOUNT FUNCTION
SPOT YIELD CURVE
IMPLIED FORWARD RATE
TERM STRUCTURE IN A CERTAIN ECONOMY
TERM STRUCTURE IN THE REAL WORLD—NOTHING IS CERTAIN
CONTINUOUS-TIME MODELS OF THE TERM STRUCTURE
DISCOUNT FUNCTION
FORWARD RATE
TERM STRUCTURE IN CONTINUOUS TIME
KEY POINTS
The Dynamic Term Structure Model
KEY ELEMENTS IN A DYNAMIC TERM STRUCTURE MODEL
EQUILIBRIUM
ARBITRAGE-FREE
CONTINUOUS TIME/CONTINUOUS STATE
COMPLETENESS OF MARKETS
DYNAMIC TERM STRUCTURE MODEL
SPOT-RATE MODEL
BOND-PRICE VALUATION MODEL
THE TERM STRUCTURE
APPLICATIONS OF THE TERM STRUCTURE MODEL
TERM STRUCTURE OF FORWARD RATES
HEATH, JARROW, AND MORTON MODEL OF THE TERM STRUCTURE
MARKET PRICE OF RISK
BOND PRICING
CHANGE OF NUMERAIRE
MARKET MODELS
INTEREST RATE DERIVATIVES
DESIGNING YOUR NEXT MODEL
KEY POINTS
Essential Classes of Interest Rate Models and Their Use
CATEGORIZATION OF APPROACHES TO TERM STRUCTURE MODELING
WHEN DO I USE EACH OF THE MODELING APPROACHES?
USING MODELS OF BORROWER BEHAVIOR WITH A RISK-NEUTRAL INTEREST RATE MODEL
KEY POINTS
NOTES
A Review of No Arbitrage Interest Rate Models
THE GENERAL MODELS FOR THE SHORT RATE
BINOMIAL AND TRINOMIAL SOLUTIONS TO THE STOCHASTIC DIFFERENTIAL EQUATIONS
COMPARATIVE STUDY OF THE NUMERICAL SOLUTIONS
APPENDIX
KEY POINTS
NOTES
Trading Cost Models
Modeling Market Impact Costs
MARKET IMPACT COSTS
LIQUIDITY AND TRANSACTION COSTS
MARKET IMPACT MEASUREMENTS AND EMPIRICAL FINDINGS
FORECASTING AND MODELING MARKET IMPACT
KEY POINTS
NOTES
Volatility
Monte Carlo Simulation in Finance
MAIN IDEAS AND IMPORTANT CONCEPTS
FINANCIAL APPLICATIONS OF SIMULATION
RANDOM NUMBER GENERATION
VARIANCE REDUCTION TECHNIQUES
SIMULATION SOFTWARE
KEY POINTS
NOTES
Stochastic Volatility
NONSTOCHASTIC VOLATILITY MEASURES
KEY POINTS
NOTES
Index
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