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

SemesterAutumn Semester 2019
LecturersK. Kirchner
Periodicityyearly recurring course
Language of instructionEnglish
CommentAlternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"



Catalogue data

AbstractCourse 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.
ObjectiveThe 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.
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
Applications to computational finance: Option valuation
Lecture notesThere will be English, typed lecture notes for registered participants in the course.
LiteratureP. 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 / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 18, 2019.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersK. Kirchner
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.
Additional information on mode of examinationLearning tasks: Meaningful solutions to 70% of the weekly homework assignments can count as bonus of up to +0.25 of final grade.

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.

Learning materials

 
Main linkCourse webpage
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-4657-00 VNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)3 hrs
Mon15-17HG D 1.2 »
Wed13-14HG E 1.1 »
K. Kirchner
401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
Groups are selected in myStudies.
1 hrs
Wed14-15HG D 7.1 »
14-15HG E 1.1 »
K. Kirchner

Groups

401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
GroupsG-01
Wed14-15HG D 7.1 »
G-02
Wed14-15HG E 1.1 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Computer Science Bachelor5. SemesterWInformation
Mathematics MasterSelection: Numerical AnalysisWInformation
Quantitative Finance MasterMathematical Methods for FinanceWInformation
Computational Science and Engineering BachelorComputational FinanceWInformation
Computational Science and Engineering MasterComputational FinanceWInformation