1   Introduction and Overview                                 
    1.A  Analytics and the Scientific Method in Finance
    1.B  Financial Models
    1.C  Empirical Studies
    1.D  Research in Finance
    1.E  Applications and Organization

2   Preliminary Analytical Concepts
    2.A  Time Value Mathematics
    2.B  Geometric Series and Expansions
           Application 2.1  Annuities and Perpetuities
           Application 2.2  Growth Models
           Application 2.3  Money and Income Multipliers
    2.C  Return Measurement
    2.D  Mean, Variance and Standard Deviation
           Application 2.4  Risk Measurement
    2.E  Comovement Statistics
           Application 2.5  Security Comovement
    2.F  Introduction to Simple OLS Regressions
           Application 2.6  Relative Risk Measurement

3   Elementary Portfolio Mathematics
    3.A  Introduction to Portfolio Analysis
    3.B  Single Index Models
    3.C  Multi-index Models

4   Matrix Mathematics
    4.A  Matrices, Vectors and Scalars
           Application 4.1  Portfolio Mathematics
    4.B  Addition, Subtraction and Transposes of Matrices
    4.C  Multiplication of Matrices
           Application 4.1 (continued)  Portfolio Mathematics
    4.D  Inversion of Matrices
    4.E  Solving Systems of Equations
           Application 4.2  Coupon Bonds and Yield Curves
           Application 4.3  Arbitrage with Riskless Bonds
           Application 4.4  Fixed Income Portfolio Dedication
    4.F  Vectors, Vector Spaces and Spanning
           Application 4.5  The State Preference Model
           Application 4.6  Binomial Option Pricing
           Application 4.7  Put-Call Parity
    4.G. Orthogonal Vectors
           Application 4.8  Arbitrage Pricing Theory

5   Differential Calculus
    5.A  Functions and Limits
           Application 5.1  The Natural Log
    5.B  Slopes, Derivatives, Maxima and Minima
           Application 5.2  Utility of Wealth
    5.C  Derivatives of Polynomials
           Application 5.3  Marginal Utility
           Application 5.4  The Baumol Cash Management Model
           Application 5.5  Duration
           Application 5.6  Bond Portfolio Immunization
           Application 5.7  Portfolio Risk and Diversification
    5.D  Partial Derivatives
           Application 5.8  Deriving the Simple OLS Regression Equation
           Application 5.9  Deriving Multiple Regression Coefficients
    5.E  The Chain Rule, Product Rule and Quotient Rule
           Application 5.10  Plotting the Capital Market Line
    5.F  Taylor Series Expansions
           Application 5.11  Convexity and Immunization
           Application 5.12  Risk Aversion Coefficients
    5.G  The Method of LaGrange Multipliers
           Application 5.13  Optimal Portfolio Selection
           Application 5.14  Plotting the Capital Market Line, Second Method
           Application 5.15  Deriving the Capital Asset Pricing Model
           Application 5.16  Constrained Utility Maximization
       Appendix 5.A  Derivatives of Polynomials
       Appendix 5.B  Rules for Finding Derivatives
       Appendix 5.C  Portfolio Risk Minimization on a Spreadsheet

6   Integral Calculus
    6.A  Antidifferentiation and the Indefinite Integral
    6.B  Definite Integrals and Areas
           Application 6.1  Cumulative Densities
           Application 6.2  Expected Value and Variance
           Application 6.3  Stochastic Dominance
           Application 6.4  Valuing Continuous Dividend Payments
           Application 6.5  Expected Option Values
    6.C  Differential Equations
           Application 6.6  Continuous Time Security Returns
       Appendix 6.A  Rules for Finding Integrals

7  Introduction to Probability
    7.A  Random Variables and Probability Spaces
    7.B  Distributions and Moments
    7.C  Binomial Distributions
           Application 7.1  Estimating Probability of Option Exercise
    7.D  The Normal Distribution
    7.E  The Log–normal Distribution
           Application 7.2  Common Stock Returns
    7.F  Conditional Probability
           Application 7.3  Option Pricing — Conditional Exercise
           Application 7.4  The Binomial Option Pricing Model

8   Statistics and Empirical Studies in Finance
    8.A  Introduction to Hypothesis Testing
           Application 8.1  Minimum Acceptable Returns
    8.B  Hypothesis Testing: Two Populations
           Application 8.2  Bank Ownership Structure
    8.C  Interpreting the Simple OLS Regression
           Application 8.3  Capital Asset Pricing Model
           Application 8.4  Analysis of Weak Form Efficiency
           Application 8.5  Portfolio Performance Evaluation
    8.D  Multiple OLS Regressions
           Application 8.6  Estimating the Yield Curve
    8.E  Event Studies
           Application 8.7  Analysis of Merger Returns
    8.F  Models with Binary Variables

9   Stochastic Processes
    9.A  Random Walks and Martingales
    9.B  Binomial Processes
    9.C  Brownian Motion, Weiner and Itô Processes
    9.D  Itô's Lemma
           Application 9.1  Geometric Weiner Processes
           Application 9.2  Option Prices — Estimating Exercise Probability
           Application 9.3  Option Prices — Estimating Expected Conditional
       Option Prices
           Application 9.4  Deriving the Black-Scholes Option Pricing Model

10   Numerical Methods
    10.A  Introduction
    10.B  The Binomial Method
           Application 10.1  The Binomial Option Pricing Model
           Application 10.2  American Put Option Valuation
    10.C  The Method of Bisection
           Application 10.3  Estimating Bond Yields
           Application 10.4  Estimating Implied Variances
    10.D  The Newton-Ralphson Method
           Application 10.4 (continued)  Estimating Implied Variances
 
Appendix A  Solutions to End-of-Chapter Exercises
Appendix B  Statistics Tables
Appendix C  Notation Definitions
Glossary
References
Index