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1 Basic Finance
2 Probability Spaces
3 Random Variables
4 Options and Arbitrage
5 Discrete-Time Portfolio Processes
6 Expectation
7 The Binomial Model
8 Conditional Expectation
9 Martingales in Discrete Time Markets
10 American Claims in Discrete-Time Markets
11 Stochastic Calculus
12 The Black-Scholes-Merton Model
13 Martingales in the Black-Scholes-Merton Model
14 Path Independent Options
15 Path Dependent Options
A Basic Combinatorics
B Solution of the BSM PDE
C Properties of the BSM Call Function
D Solutions to Odd-Numbered Problems

Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives.

The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time.

The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model.

The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author's webpage https://home.gwu.edu/~hdj/.