Modul

oral exam of ca. 30 minutes

The lecture concentrates on option pricing with numerical methods.

After participation, students

• know how to model the price dynamics of different types of options by stochastic or partial differential equations, and to evaluate the differences between these models.
• know, in particular, the assumptions on which these models are based, which enables them to discuss and question the meaningfulness and reliability of the models.
• know different methods for solving stochastic and partial differential equations numerically, and for solving high-dimensional integration problems.
• are able to implement and apply these methods to different types of options, and to analyze their stability and convergence.

none

• Options, arbitrage and other basic concepts,
• Black-Scholes equation und Black-Scholes formulas,
• Numerical methods for stochastic differential equations,
• (Multilevel) Monte Carlo methods,
• (Quasi-)Monte Carlo integration,
• Numerical methods for Black-Scholes equations,
• Numerical methods for American options

Familiarity with stochastic differential equations, the Ito integral, and the Ito formula is strongly recommended. MATLAB skills are strongly recommended for the programming exercises.

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination