The course "Numerical Finance" consists of two 2-hour lectures and one 2-hour exercise per week.

• Exam form is oral.

• Generation of random numbers
• Monte-Carlo and Quasi-Monte-Carlo methods
• Numerical methods for the computation of European and American options: Binomial, Finite Difference and Finite Element methods
• Numerical methods for the simulation of stochastic processes: numerical treatment of stochastic differential equations

The course focusses both on the theoretical foundations and the practical aspects of the numerical methods. The underlying financial models will not be discussed in detail, a slight background in finance is therefore advisable. The exercises contain both theoretical work as well as the implementation (in C++) of the numerical approaches.

The exam form is oral. Before registering for the exam, you have to register for and pass the exercises. At the end of the semester and after passing the exercises, you have to register for the exam and arrange an appointment for oral examination with Petra Hildebrand.

Exercises will take place Thursdays every week.

See also the bibliography of the lecture notes.

• R. Seydel, Tools for Computational Finance, Springer 2006
• M. Günther, A. Jüngel, Finanzderivate mit Matlab, Vieweg 2003
• L.C.G. Rogers, D. Talay, Numerical Methods in Finance, 1997
• P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer 1999

 There is a huge amount of literature for C++ available. Good starting points are:

• C++ Language Tutorial
• C++ Online References
• stackoverflow.com (forum with usually very qualified answers).
• "Thinking in C++" by Bruce Eckel. Exhaustive and detailed free book in 2 parts, with very good explanations. Here as PDF.