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