1. Introduction and Overview:.
The Importance of Mathematics in Finance.
Mathematical and Computer Modeling in Finance.
Money, Securities, and Markets.
Time Value, Risk, Arbitrage, and Pricing.
The Organization of this Book.
2. Review of Elementary Mathematics: Functions and Operations:.
Variables, Equations, and Inequalities.
The Order of Arithmetic Operations and the Rules of Algebra.
The Number e.
Permutations and Combinations.
Appendix: An Introduction to the ExcelT Spreadsheet.
3. A Review of Elementary Mathematics: Algebra and Solving Equations:.
The Quadratic Formula.
Solving Systems of Equations that Contain Multiple Variables.
Functions and Graphs.
Appendix: Solving Systems of Equations on a Spreadsheet.
4. The Time Value of Money:.
Introduction and Future Value.
Fractional Period Compounding of Interest.
Continuous Compounding of Interest.
Annuity Future Values.
Discounting and Present Value.
Present Value of a Series of Cash Flows.
Annuity Present Values.
Single-stage Growth Models.
Multiple-stage Growth Models.
Appendix: Time Value Spreadsheet Applications.
5. Return, Risk, and Co-movement:.
Return on Investment.
Geometric Mean Return on Investment.
Internal Rate of Return.
An Introduction to Risk.
Variance and Standard Deviation.
Historical Variance and Standard Deviation.
The Coefficient of Correlation and the Coefficient of Determination.
Appendix: Return and Risk Spreadsheet Applications.
6. Elementary Portfolio Mathematics:.
An Introduction to Portfolio Analysis.
Diversification and Efficiency.
The Market Portfolio and Beta.
Deriving the Portfolio Variance Expression.
7. Elements of Matrix Mathematics:.
An Introduction to Matrices.
Solving Systems of Equations.
Spanning the State Space.
Appendix: Matrix mathematics on a Spreadsheet.
8. Differential Calculus:.
Functions and Limits.
Slopes, Derivatives, Maxima, and Minima.
Derivatives of Polynomials.
Partial and Total Derivatives.
The Chain Rule, Product Rule, and Quotient Rule.
Logarithmic and Exponential Functions.
Taylor Series Expansions.
The Method of LaGrange Multipliers.
Appendix: Derivatives of Polynomials.
Appendix: A Table of Rules for Finding Derivatives.
Appendix: Portfolio Risk Minimization on a Spreadsheet.
9. Integral Calculus:.
Antidifferentiation and the Indefinite Integral.
Definite Integrals and Areas.
Appendix: Rules for Finding Integrals.
Appendix: Riemann sums on a spreadsheet.
10. Elements of Options Mathematics:.
An Introduction to Stock Options.
Binomial Option Pricing: One Time Period.
Binomial Option Pricing: Multiple Time Periods.
The Black–Scholes Option Pricing Model.
Puts and Valuation.
Black–Scholes Model Sensitivities.
Estimating Implied Volatilities.
Appendix A: Solutions to Exercises.
Appendix B: The z-Table.
Appendix C: Notation.
Appendix D: Glossary.