After successful completion of the course, students are able to develop models for a financial market und for financial derivates, to calculate the value of European and some exotic options by binomial and Monte-Carlo Methods and to solve stochastic differential equations and the obstacle problem for American options.

Ito-formula, Black-scholes model and its extensions, binomial methods, Monte-Carlo methods, finite-difference methods, American options as free boundary problems, applications: call options on Bitcoin, Asian options, swing options in electricity markets

There will be lectures and exercises. In the lecture the theory will be introduced and examples will be calculated. There will be weekly exercise-sheets  which will have to be calculated by the students during the lecture.

oral exam

Lecture notes are available at https://www.asc.tuwien.ac.at/~juengel -> Teaching -> Lecture Notes

Analysis, ordinary differential equations, basics of probability theory. Stochastic analysis and partial differential equations are not assumed