• The exercise class has been moved to Wednesday, 12:15 - 14:00, He18, E44.
• Please register in the SLC system for the exercises. The same account gives access to the computers in the IAI pools (e.g. He18 E44), so if you have one, you most likely have the other as well. Please check both before the first exercise class.

Type

Lecture with exercise classes (4/2), both will be held in English.

Responsible

• Prof. Dr. Karsten Urban
• Dipl.-Math. oec. Kristina Steih

Relevant for

• Master of Finance
• Master / Diplom Wirtschaftsmathematik
• Master / Diplom Mathematik

Exam:

• Oral exam
• required: active participation in programming exercises (Leistungsnachweis)

Classification:

• Finanzmathematik
• Numerik

• Financial Mathematics
• Mathematics

• 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.

• Tuesday, 12:00 - 14:00, He 18, room 220
• Wednesday, 10:00 - 12:00, He 18, room 220

Lectures will start on Tuesday, April 22nd.

The access to the lecture notes is restricted to the university subnet.

• Wednesday, 12:00 - 14:00, He 18, room E44

Exercises will start on Friday, April 25th, with a C++ training class. We will meet in the computer pool E44, He 18 (next to the library).

Exercises points will be managed using the SLC, so please register there for the lecture. The same account gives access to the computers in the IAI pools (e.g. He18 E44), so if you have one, you most likely have the other as well. Please check both before the first exercise class.

Additional material and the solutions to the programming exercises are only accessible from the university subnet.

Exercise Sheet C++ Warmup C++ Checklist

Exercise Sheet 1 (Note: You do not have to compute the Chi2-quantiles in the programming exercise 2 - please use tabulated values or similar)

Exercise Sheet 2

Exercise Sheet 3

Exercise Sheet 4 (Correction: The interval length in the Composite Simpson's rule is of course h=1/n)

Exercise Sheet 5 (Correction: In the price of a digital option, the discount factor should involve the remaining time to maturity of the option, i.e. exp(-r(T-t)), not exp(-rt).)

Exercise Sheet 6

Exercise Sheet 7

Exercise Sheet 8

Exercise Sheet 9 (Corrections: Typos in the Dirichlet BC hints to the Prog. Ex. 1)

Exercise Sheet 10 (Comment: You can solve Exercise 2 even if Exercise 1 does not work correctly -- just use the already refined mesh given in the material)

Exercise Sheet 11

Additionally, here is a checklist with questions that you can use to see whether you have understood the different aspects of the lecture when preparing for the oral exam.

There will be oral exams at the end of the semester.

For the admission to these exams (Leistungsnachweis), we require an active participation in the exercises (probably at least 50% of the programming exercise points, the exact organization will depend on the number of participants).

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 HTML with code examples, here as PDF.