An Undergraduate Introduction to Financial Mathematics

The following sections are included:

• Preface

• Preface to the First Edition

• Contents

The following sections are included:

• Simple Interest

• Compound Interest

• Continuously Compounded Interest

• Present Value

• Rate of Return

• Exercises

The following sections are included:

• Events and Probabilities

• Addition Rule

• Conditional Probability and Multiplication Rule

• Random Variables and Probability Distributions

• Binomial Random Variables

• Expected Value

• Variance and Standard Deviation

• Exercises

The following sections are included:

• Continuous Random Variables

• Expected Value of Continuous Random Variables

• Variance and Standard Deviation

• Normal Random Variables

• Central Limit Theorem

• Lognormal Random Variables

• Properties of Expected Value

• Properties of Variance

• Exercises

The following sections are included:

• The Concept of Arbitrage

• Duality Theorem of Linear Programming
  • Dual Problems

• The Fundamental Theorem of Finance

• Exercises

The following sections are included:

• Intuitive Idea of a Random Walk

• First Step Analysis

• Intuitive Idea of a Stochastic Process

• Itô Processes

• Itô's Lemma

• Stock Market Example

• Exercises

The following sections are included:

• Definition of a Forward Contract

• Pricing a Forward Contract

• Dividends and Pricing

• Incorporating Transaction Costs

• Futures

• Exercises

The following sections are included:

• Properties of Options

• Pricing an Option Using a Binary Model

• Black-Scholes Partial Differential Equation

• Boundary and Initial Conditions

• Exercises

The following sections are included:

• Fourier Transforms

• Inverse Fourier Transforms

• Changing Variables in the Black-Scholes PDE

• Solving the Black-Scholes Equation

• Binomial Model (Optional)

• Exercises

The following sections are included:

• Theta

• Delta

• Gamma

• Vega

• Rho

• Relationships Between Δ, ⊗, and Γ

• Exercises

The following sections are included:

• General Principles

• Delta Hedging

• Delta Neutral Portfolios

• Gamma Neutral Portfolios

• Exercises

The following sections are included:

• Covariance and Correlation

• Optimal Portfolios

• Utility Functions

• Expected Utility

• Portfolio Selection

• Minimum Variance Analysis

• Mean-Variance Analysis

• Exercises

The following sections are included:

• Parity and American Options

• American Puts Valued by a Binomial Model

• Properties of the Binomial Pricing Formula

• Optimal Exercise Time

• Exercises

The following sections are included:

• Appendix A Sample Stock Market Data

• Appendix B Solutions to Chapter Exercises

• Bibliography

• Index