401-4657-00L  Numerical Analysis of Stochastic Ordinary Differential Equations

SemesterAutumn Semester 2012
LecturersA. Jentzen
Periodicityyearly recurring course
Language of instructionEnglish
CommentAlternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"



Courses

NumberTitleHoursLecturers
401-4657-00 VNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)3 hrs
Wed13:15-15:00HG E 1.1 »
Fri13:15-14:00HG E 1.1 »
A. Jentzen
401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)1 hrs
Fri14:15-15:00HG E 1.1 »
A. Jentzen

Catalogue data

AbstractCourse 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.
ObjectiveThe 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.
ContentGeneration 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 notesPrinted Lecture Notes on the class material will be
distributed in class.
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering,
Springer Verlag 2004.

P. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations
Springer Verlag.
Prerequisites / NoticePrerequisites:

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 credits6 credits
ExaminersA. Jentzen
Typeend-of-semester examination
Language of examinationEnglish
RepetitionThe performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Admission requirementA 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 examinationEnd-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

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Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics MasterSelection: Numerical AnalysisWInformation
Quantitative Finance MasterMathematical Methods for FinanceWInformation
Computational Science and Engineering MasterFinancial EngineeringWInformation