Elementary introduction which uses only plus and minus as basic mathematical operations;

a 1-period model with two outcomes, up or down.

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)

Chapter 1: Trading Strategies

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

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

Chapter A1: American Options in the Binomial Model

Chapter A2: American Options in the Black-Scholes Model

List with References

ItoFormula_Simulation.xlsm

BlackScholes_Analytic_vs_MonteCarlo.xlsm

Down-and-Out-BarrierCall_Analytic_vs_MonteCarlo.xlsm

OrnsteinUhlenbeck-Heston-GarchDiffusion.xlsm

University of Applied Sciences:

Bachelor and Master Program in Applied Mathematics:

- Online Application
- International Students
- Bachelor Program Applied Mathematics (in german)
- Master Program Applied Mathematics (in german)

Option Pricing

Time Series Models

**Hochschule RheinMain, **

Applied Mathematics:

Time Series Models

Applied Mathematics:

- Online Application
- International Students
- Bachelor Program Applied Mathematics
- Master Program Applied Mathematics