401-4657-00L Numerical Analysis of Stochastic Ordinary Differential Equations
Semester | Autumn Semester 2012 |
Lecturers | A. Jentzen |
Periodicity | yearly recurring course |
Language of instruction | English |
Comment | Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" |
Courses
Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|
401-4657-00 V | Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods) | 3 hrs |
| A. Jentzen | ||||||
401-4657-00 U | Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods) | 1 hrs |
| A. Jentzen |
Catalogue data
Abstract | Course on numerical approximation 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 of 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 | Printed Lecture Notes on the class material will be distributed in class. |
Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering, Springer Verlag 2004. P. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations Springer Verlag. |
Prerequisites / Notice | Prerequisites: a) mandatory courses: Elementary Probability, Probability Theory I, MATLAB programming. b) recommended courses: Stochastic Processes. |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
ECTS credits | 6 credits |
Examiners | A. Jentzen |
Type | end-of-semester examination |
Language of examination | English |
Repetition | The performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling. |
Admission requirement | A NUMERICAL GRADE for the course is based only on the written End-of-Semester final examination. Participation in the written End-of-Semester final examination requires ``TESTAT''. A ``TESTAT'' constitutes ``successful participation in course''. It is NOT a numerical grade. ``TESTAT'' is given if correct solution of at least 70 per cent of COURSE HOMEWORK ASSIGNMENTS has been achieved. |
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 under LINUX. Own computer will NOT be required for the examination. |
Learning materials
No public learning materials available. | |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |
Offered in
Programme | Section | Type | |
---|---|---|---|
Mathematics Master | Selection: Numerical Analysis | W | |
Quantitative Finance Master | Mathematical Methods for Finance | W | |
Computational Science and Engineering Master | Financial Engineering | W |