The mathematics of financial modeling and investment management

The Mathematics Of Financial Modeling And Investment Management

The Mathematics Of Financial Modeling And Investment Management by Sergio M. Focardi and Frank J. Fabozzi

Contents of Mathematics Of Financial Modeling eBook

  • CHAPTER 1. From Art to Engineering in Finance
  • Investment Management Process
  • Step : Setting Investment Objectives
  • Step : Establishing an Investment Policy
  • Step : Selecting a Portfolio Strategy
  • Step : Selecting the Specific Assets
  • Step : Measuring and Evaluating Performance
  • Financial Engineering in Historical Perspective
  • The Role of Information Technology
  • Industry’s Evaluation of Modeling Tools
  • Integrating Qualitative and Quantitative Information
  • Principles for Engineering a Suite of Models
  • Summary
  • CHAPTER 2. Overview of Financial Markets, Financial Assets, and Market Participants
  • Financial Assets
  • Financial Markets
  • Classification of Financial Markets
  • Economic Functions of Financial Markets
  • Secondary Markets
  • Overview of Market Participants
  • Role of Financial Intermediaries
  • Institutional Investors
  • Insurance Companies
  • Pension Funds
  • Investment Companies
  • Depository Institutions
  • Endowments and Foundations
  • Common Stock
  • Trading Locations
  • Stock Market Indicators
  • Trading Arrangements
  • Bonds
  • Maturity
  • Par Value
  • Coupon Rate
  • Provisions for Paying off Bonds
  • Options Granted to Bondholders
  • Futures and Forward Contracts
  • Futures versus Forward Contracts
  • Risk and Return Characteristics of Futures Contracts
  • Pricing of Futures Contracts
  • The Role of Futures in Financial Markets
  • Options
  • Risk-Return for Options
  • The Option Price
  • Swaps
  • Caps and Floors
  • Summary
  • CHAPTER 3. Milestones in Financial Modeling and Investment Management
  • 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
  • Modigliani-Miller Irrelevance Theorems and the
  • Absence of Arbitrage
  • 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
  • Summary
  • CHAPTER 4. Principles of Calculus
  • Sets and Set Operations
  • Proper Subsets
  • Empty Sets
  • Union of Sets
  • Intersection of Sets
  • Elementary Properties of Sets
  • Distances and Quantities
  • n-tuples
  • Distance
  • Density of Points
  • Functions
  • Variables
  • Limits
  • Continuity
  • Total Variation
  • Differentiation
  • Commonly Used Rules for Computing Derivatives
  • Higher Order Derivatives
  • Application to Bond Analysis
  • Taylor Series Expansion
  • Application to Bond Analysis
  • Integration
  • Riemann Integrals
  • Properties of Riemann Integrals
  • Lebesque-Stieltjes Integrals
  • Indefinite and Improper Integrals
  • The Fundamental Theorem of Calculus
  • Integral Transforms
  • Laplace Transform
  • Fourier Transforms
  • Calculus in More than One Variable
  • Summary
  • CHAPTER 5. Matrix Algebra
  • Vectors and Matrices Defined
  • Vectors
  • Matrices
  • Square Matrices
  • Diagonals and Antidiagonals
  • Identity Matrix
  • Diagonal Matrix
  • Upper and Lower Triangular Matrix
  • Determinants
  • Systems of Linear Equations
  • Linear Independence and Rank
  • Hankel Matrix
  • Vector and Matrix Operations
  • Vector Operations
  • Matrix Operations
  • Eigenvalues and Eigenvectors
  • Diagonalization and Similarity
  • Singular Value Decomposition
  • Summary
  • CHAPTER 6. Concepts of Probability
  • Representing Uncertainty with Mathematics
  • Probability in a Nutshell
  • Outcomes and Events
  • Probability
  • Measure
  • Random Variables
  • Integrals
  • Distributions and Distribution Functions
  • Random Vectors
  • Stochastic Processes
  • Probabilistic Representation of Financial Markets
  • Information Structures
  • Filtration
  • Conditional Probability and Conditional Expectation
  • Moments and Correlation
  • Copula Functions
  • Sequences of Random Variables
  • Independent and Identically Distributed Sequences
  • Sum of Variables
  • Gaussian Variables
  • The Regression Function
  • Linear Regression
  • Summary
  • CHAPTER 7. Optimization
  • Maxima and Minima
  • Lagrange Multipliers
  • Numerical Algorithms
  • Linear Programming
  • Quadratic Programming
  • Calculus of Variations and Optimal Control Theory
  • Stochastic Programming
  • Summary
  • CHAPTER 8. Stochastic Integrals
  • The Intuition Behind Stochastic Integrals
  • Brownian Motion Defined
  • Properties of Brownian Motion
  • Stochastic Integrals Defined
  • Some Properties of Itô Stochastic Integrals
  • Summary
  • CHAPTER 9. Differential Equations and Difference Equations
  • Differential Equations Defined
  • Ordinary Differential Equations
  • Order and Degree of an ODE
  • Solution to an ODE
  • Systems of Ordinary Differential Equations
  • Closed-Form Solutions of Ordinary Differential Equations
  • Linear Differential Equation
  • Numerical Solutions of Ordinary Differential Equations
  • The Finite Difference Method
  • Nonlinear Dynamics and Chaos
  • Fractals
  • Partial Differential Equations
  • Diffusion Equation
  • Solution of the Diffusion Equation
  • Numerical Solution of PDEs
  • Summary
  • CHAPTER 10. Stochastic Differential Equations
  • The Intuition Behind Stochastic Differential Equations
  • The -Dimensional Formula
  • Stochastic Differential Equations
  • Generalization to Several Dimensions
  • Solution of Stochastic Differential Equations
  • The Arithmetic Brownian Motion
  • The Ornstein-Uhlenbeck Process
  • The Geometric Brownian Motion
  • Summary
  • CHAPTER 11. Financial Econometrics: 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
  • Univariate Stationary Series
  • The Lag Operator L
  • Stationary Univariate Moving Average
  • Multivariate Stationary Series
  • Nonstationary Series
  • ARMA Representations
  • Stationary Univariate ARMA Models
  • Nonstationary Univariate ARMA Models
  • Stationary Multivariate ARMA Models
  • Nonstationary Multivariate ARMA Models
  • Markov Coefficients and ARMA Models
  • Hankel Matrices and ARMA Models
  • State-Space Representation
  • Equivalence of State-Space and ARMA Representations
  • Integrated Series and Trends
  • Summary
  • CHAPTER 12. Financial Econometrics: Model Selection, Estimation, and Testing
  • Model Selection
  • Learning and Model Complexity
  • Maximum Likelihood Estimate
  • Linear Models of Financial Time Series
  • Random Walk Models
  • Correlation
  • Random Matrices
  • Multifactor Models
  • CAPM
  • Asset Pricing Theory (APT) Models
  • PCA and Factor Models
  • Vector Autoregressive Models
  • Cointegration
  • State-Space Modeling and Cointegration
  • Empirical Evidence of Cointegration in Equity Prices
  • Nonstationary Models of Financial Time Series
  • The ARCH/GARCH Family of Models
  • Markov Switching Models
  • Summary
  • CHAPTER 13. Fat Tails, Scaling, and Stable Laws
  • Scaling, Stable Laws, and Fat Tails
  • Fat Tails
  • The Class L of Fat-Tailed Distributions
  • The Law of Large Numbers and the Central Limit Theorem
  • Stable Distributions
  • Extreme Value Theory for IID Processes
  • Maxima
  • Max-Stable Distributions
  • Generalized Extreme Value Distributions
  • Order Statistics
  • Point Process of Exceedances or Peaks over Threshold
  • Estimation
  • Eliminating the Assumption of IID Sequences
  • Heavy-Tailed ARMA Processes
  • ARCH/GARCH Processes
  • Subordinated Processes
  • Markov Switching Models
  • Estimation
  • Scaling and Self-Similarity
  • Evidence of Fat Tails in Financial Variables
  • On the Applicability of Extreme Value Theory in Finance
  • Summary
  • CHAPTER 14. Arbitrage Pricing: Finite-State Models
  • The Arbitrage Principle
  • Arbitrage Pricing in a One-Period Setting
  • State Prices
  • Risk-Neutral Probabilities
  • Complete Markets
  • Arbitrage Pricing in a Multiperiod Finite-State Setting
  • Propagation of Information
  • Trading Strategies
  • State-Price Deflator
  • Pricing Relationships
  • Equivalent Martingale Measures
  • Risk-Neutral Probabilities
  • Path Dependence and Markov Models
  • The Binomial Model
  • Risk-Neutral Probabilities for the Binomial Model
  • Valuation of European Simple Derivatives
  • Valuation of American Options
  • Arbitrage Pricing in a Discrete-Time, Continuous-State Setting
  • APT Models
  • Testing APT
  • Summary
  • CHAPTER 15. Arbitrage Pricing: Continuous-State, Continuous-Time Models
  • The Arbitrage Principle in Continuous Time
  • Trading Strategies and Trading Gains
  • Arbitrage Pricing in Continuous-State, Continuous-Time
  • Option Pricing
  • Stock Price Processes
  • Hedging
  • The Black-Scholes Option Pricing Formula
  • Generalizing the Pricing of European Options
  • State-Price Deflators
  • Equivalent Martingale Measures
  • Equivalent Martingale Measures and Girsanov’s Theorem
  • The Diffusion Invariance Principle
  • Application of Girsanov’s Theorem to Black-Scholes
  • Option Pricing Formula
  • 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
  • Summary
  • CHAPTER 16. Portfolio Selection Using Mean-Variance Analysis
  • Diversification as a Central Theme in Finance
  • Markowitz’s Mean-Variance Analysis
  • Capital Market Line
  • Deriving the Capital Market Line
  • What is Portfolio M?
  • Risk Premium in the CML
  • The CML and the Optimal Portfolio
  • Utility Functions and Indifference Curves
  • Selection of the Optimal Portfolio
  • Extension of the Markowitz Mean-Variance Model to
  • Inequality Constraints
  • A Second Look at Portfolio Choice
  • The Return Forecast
  • The Utility Function
  • Optimizers
  • A Global Probabilistic Framework for Portfolio Selection
  • Relaxing the Assumption of Normality
  • Multiperiod Stochastic Optimization
  • Application to the Asset Allocation Decision
  • The Inputs
  • Portfolio Selection: An Example
  • Inclusion of More Asset Classes
  • Extensions of the Basic Asset Allocation Model
  • Summary
  • CHAPTER 17. Capital Asset Pricing Model
  • CAPM Assumptions
  • Systematic and Nonsystematic Risk
  • Security Market Line
  • Estimating the Characteristic Line
  • Testing The CAPM
  • Deriving the Empirical Analogue of the CML
  • Empricial Implications
  • General Findings of Empirical Tests of the CAPM
  • A Critique of Tests of the CAPM
  • Merton and Black Modifications of the CAPM
  • CAPM and Random Matrices
  • The Conditional CAPM
  • Beta, Beta Everywhere
  • The Role of the CAPM in Investment Management Applications
  • Summary
  • CHAPTER 18. Multifactor Models and Common Trends for Common Stocks
  • Multifactor Models
  • Determination of Factors
  • Dynamic Market Models of Returns
  • Estimation of State-Space Models
  • Dynamic Models for Prices
  • Estimation and Testing of Cointegrated Systems
  • Cointegration and Financial Time Series
  • Nonlinear Dynamic Models for Prices and Returns
  • Summary
  • CHAPTER 19. Equity Portfolio Management
  • Integrating the Equity Portfolio Management Process
  • Active versus Passive Portfolio Management
  • Tracking Error
  • Backward-Looking versus Forward-Looking Tracking Error
  • The Impact of Portfolio Size, Benchmark Volatility, and
  • Portfolio Beta on Tracking Error
  • Equity Style Management
  • Types of Equity Styles
  • Style Classification Systems
  • Passive Strategies
  • Constructing an Indexed Portfolio
  • Index Tracking and Cointegration
  • Active Investing
  • Top-Down Approaches to Active Investing
  • Bottom-Up Approaches to Active Investing
  • Fundamental Law of Active Management
  • Strategies Based on Technical Analysis
  • Nonlinear Dynamic Models and Chaos
  • Technical Analysis and Statistical Nonlinear
  • Pattern Recognition
  • Market-Neutral Strategies and Statistical Arbitrage
  • Application of Multifactor Risk Models
  • Risk Decomposition
  • Portfolio Construction and Risk Control
  • Assessing the Exposure of a Portfolio
  • Risk Control Against a Stock Market Index
  • Tilting a Portfolio
  • Summary
  • CHAPTER 20. Term Structure Modeling and Valuation of Bonds and Bond Options
  • Basic Principles of Valuation of Debt Instruments
  • Yield-to-Maturity Measure
  • Premium Par Yield
  • Reinvestment of Cash Flow and Yield
  • The Term Structure of the Interest Rates and the Yield Curve
  • Limitations of Using the Yield to Value a Bond
  • Valuing a Bond as a Package of Cash Flows
  • Obtaining Spot Rates from the Treasury Yield Curve
  • Using Spot Rates to the Arbitrage-Free Value of a Bond
  • The Discount Function
  • Forward Rates
  • Swap Curve
  • Classical Economic Theories About the Determinants of the
  • Shape of the Term Structure
  • Expectations Theories
  • Market Segmentation Theory
  • Bond Valuation Formulas in Continuous Time
  • The Term Structure of Interest Rates in Continuous Time
  • Spot Rates: Continuous Case
  • Forward Rates: Continuous Case
  • Relationships for Bond and Option Valuation
  • The Feynman-Kac Formula
  • Multifactor Term Structure Model
  • Arbitrage-Free Models versus Equilibrium Models
  • Examples of One-Factor Term Structure Models
  • Two-Factor Models
  • Pricing of Interest-Rate Derivatives
  • The Heath-Jarrow-Morton Model of the Term Structure
  • The Brace-Gatarek-Musiela Model
  • Discretization of Itô Processes
  • Summary
  • CHAPTER 21. Bond Portfolio Management
  • Management versus a Bond Market Index
  • Tracking Error and Bond Portfolio Strategies
  • Risk Factors and Portfolio Management Strategies
  • Determinants of Tracking Error
  • Illustration of the Multifactor Risk Model
  • Liability-Funding Strategies
  • Cash Flow Matching
  • Portfolio Immunization
  • Scenario Optimization
  • Stochastic Programming
  • Summary
  • CHAPTER 22. Credit Risk Modeling and Credit Default Swaps
  • Credit Default Swaps
  • Single-Name Credit Default Swaps
  • Basket Default Swaps
  • Legal Documentation
  • Credit Risk Modeling: Structural Models
  • The Black-Scholes-Merton Model
  • Geske Compound Option Model
  • Barrier Structural Models
  • Advantages and Drawbacks of Structural Models
  • Credit Risk Modeling: Reduced Form Models
  • The Poisson Process
  • The Jarrow-Turnbull Model
  • Transition Matrix
  • The Duffie-Singleton Model
  • General Observations on Reduced Form Models
  • Pricing Single-Name Credit Default Swaps
  • General Framework
  • Survival Probability and Forward Default Probability:
  • A Recap
  • Credit Default Swap Value
  • No Need For Stochastic Hazard Rate or Interest Rate
  • Delivery Option in Default Swaps
  • Default Swaps with Counterparty Risk
  • Valuing Basket Default Swaps
  • The Pricing Model
  • How to Model Correlated Default Processes
  • Summary
  • CHAPTER 23. Risk Management
  • Market Completeness
  • The Mathematics of Market Completeness
  • The Economics of Market Completeness
  • Why Manage Risk?
  • Risk Models
  • Market Risk
  • Credit Risk
  • Operational Risk
  • Risk Measures
  • Risk Management in Asset and Portfolio Management
  • Factors Driving Risk Management
  • Risk Measurement in Practice
  • Getting Down to the Lowest Level
  • Regulatory Implications of Risk Measurement
  • Summary

Request your PDF Book

Write the name of the book in detail (Name, Author, Edition...)

What's the problem with this file?