An introduction to option pricing theory and risk management in the discrete-time, binomial tree model, and the continuous-time Black-Scholes-Merton framework. Both the partial differential equations approach and the martingale approach (risk-neutral pricing by expected values) will be developed. The course will cover the basics of Stochastic, Ito Calculus. Since 2015, the course is offered in the flipped format: the students are required to watch lectures online, while problem solving and case and paper presentations are done in class.