Junghenn H. An Introduction to Financial Mathematics. Option Valuation 2ed 2019

Textbook in PDF format

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 ?fteen chapters, the ?rst ten of which develop option valuation techniques in discrete time, the last ?ve 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.
Basic Finance
Probability Spaces
Random Variables
Options and Arbitrage
Discrete-Time Portfolio Processes
Expectation
The Binomial Model
Conditional Expectation
Martingales in Discrete Time Markets
American Claims in Discrete-Time Markets
Stochastic Calculus
The Black-Scholes-Merton Model
Martingales in the Black-Scholes-Merton Model
Path-Independent Options
Path-Dependent Options
Applications
Basic Combinatorics
Solution of the BSM PDE
Properties of the BSM Call Function
Solutions to Odd-Numbered Problems