Option Pricing, the Basic Idea:

The Main Idea: Replication of Financial Derivatives
Elementary introduction which uses only plus and minus as basic mathematical operations;
a 1-period model with two outcomes, up or down.

Option Pricing by Example:

An Excel-Demo which replicates an arbitrary user-defined payoff in a 4-period model
A replicating hedge portfolio is set up. The costs to set up this portfolio is the option price.
The market moves can be chosen by the user and after each market move, the p&l of the
hedge portfolio is displayed. At maturity, the hedge portfolio has replicated the option payoff.
(screenshot example)

Option Pricing Step by Step:

The Black-Scholes World:
Chapter 2: The Binomial Model
Chapter 3: Real World and Risk Neutral Probabilities
Chapter 4: Brownian Motion, Wiener Measure and the Black-Scholes Model
Chapter 5: The Black-Scholes Model as Continuous Time Limit of the Binomial Model
Chapter 6: Price and Greeks of Call and Put Options and the Black-Scholes Formula
Chapter 7: The Black-Scholes Equation
Chapter 8: Stochastic Calculus and the Ito-Formula
Chapter 9: The Risk Neutral Pricing Measure for the Black-Scholes Model
Chapter 10: Probabilities Involving the Minimum and the Maximum of a Brownian Motion
Chapter 11: Barrier and Lookback Options in the Black-Scholes Model
Chapter 12: Calculation of Expectation Values: The Monte Carlo Method
Chapter 13: The Time-Dependent Black-Scholes Model and Calibration to Market
Chapter 14: The Multi-Underlying Black-Scholes Model and Correlation

Extensions of Black-Scholes:
Chapter 15: Ito-Diffusions and the Ornstein-Uhlenbeck Process
Chapter 16: Girsanov's Theorem for Ito-Diffusions
Chapter 17: The Feynman-Kac Formula
Chapter 18: Pricing and Hedging in the Presence of Stochastic Volatility and Stochastic Interest Rates
Chapter 19: The Black-Scholes-Vasicek Model
Chapter 20: Bessel Processes
Chapter 21: The Cox-Ingersoll-Ross Process
Chapter 22: Stochastic Volatility Models
Chapter 23: The Heston Model

American Options:
Chapter A1: American Options in the Binomial Model
Chapter A2: American Options in the Black-Scholes Model

References:
List with References

Hochschule RheinMain Wiesbaden Rüsselsheim, Prof. Dr. D. Lehmann, Studiengang Angewandte Mathematik