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