401-4657-00L Numerical Analysis of Stochastic Ordinary Differential Equations
|Semester||Autumn Semester 2016|
|Periodicity||yearly recurring course|
|Language of instruction||English|
|Comment||Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"|
|Abstract||Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.|
|Objective||The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.|
|Content||Generation of random numbers|
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
|Lecture notes||Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).|
|Literature||P. Glassermann: |
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.
P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
|Prerequisites / Notice||Prerequisites:|
Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.
a) mandatory courses:
Probability Theory I.
b) recommended courses:
Start of lectures: Wednesday, September 21, 2016
For more details, please follow the link in the Learning materials section.
|Performance assessment information (valid until the course unit is held again)|
|Performance assessment as a semester course|
|ECTS credits||6 credits|
|Language of examination||English|
|Repetition||The performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.|
|Additional information on mode of examination||End-of-Semester examination will be *closed book*, 2hr in class, and will involve theoretical as well as MATLAB programming problems.|
Examination will take place on ETH-workstations running MATLAB.
Own computer will NOT be allowed for the examination.
|Online examination||The examination may take place on the computer.|
|Main link||Lecture homepage|
|Only public learning materials are listed.|
|401-4657-00 V||Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)||3 hrs|
|401-4657-00 U||Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)|
Thu 14-15 or Fri 12-13
|No information on groups available.|
|There are no additional restrictions for the registration.|