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

SemesterAutumn Semester 2021
LecturersA. Stein
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
Mon16:15-18:00HG D 1.2 »
Wed14:15-15:00HG D 5.2 »
A. Stein
401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
Groups are selected in myStudies.
1 hrs
Wed15:15-16:00HG D 5.2 »
15:15-16:00LFW C 1 »
A. Stein

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/Python programming.

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

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday September 22, 2021.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersA. Stein
Typeend-of-semester examination
Language of examinationEnglish
RepetitionA repetition date will be offered in the first two weeks of the semester immediately consecutive.
Mode of examinationwritten 120 minutes
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/Python programming problems.
Examination will take place on ETH-workstations running MATLAB/Python.
Own computer will NOT be allowed for the examination.
Written aidsNone
Online examinationThe examination may take place on the computer.
Distance examinationIt is not possible to take a distance examination.

Learning materials

No public learning materials available.
Only public learning materials are listed.

Groups

401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
GroupsG-01
Wed15:15-16:00LFW C 1 »
G-02
Wed15:15-16:00HG D 5.2 »

Restrictions

PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupDoctorate Architecture (064002)
Doctorate Architecture (064002)
Doctorate Civil Engineering (114102)
Doctorate Environmental Engineering (114202)
Doctorate Geomatic Engineering (114302)
Doctorate Mechanical and Process Engineering (164002)
Doctorate Inform. Tech. & Electrical Engineering (239002)
Doctorate Inform. Tech. & El. Engineering ETH-UZH (241000)
Doctorate Inform. Tech. & El. Engineering UZH-ETH (241100)
Computer Science MSc (263000)
Doctorate Computer Science (264002)
Doctorate Materials (339002)
Doctorate Management, Technology, and Economics (364002)
Doctorate Health Sciences and Technology (389000)
Doctorate Food Sciences (389100)
Doctorate Health Sciences and Technology ETH-UZH (390000)
Doctorate Health Sciences and Technology UZH-ETH (390100)
Mathematics BSc (404000) starting semester 05
Computational Science and Engineering BSc (406000) starting semester 05
Quantitative Finance MSc (435000)
Mathematics MSc (437000)
Applied Mathematics MSc (437100)
Computational Science and Engineering MSc (438000)
Doctorate Mathematics (439002)
Doctorate Physics (464002)
Doctorate Chemistry (539002)
Doctorate Chemical Engineering (539102)
Doctorate Interdisciplinary Sciences (539202)
Doctorate Pharmaceutical Sciences (539302)
Doctorate Biology (564002)
Doctorate Biology ETH-UZH (565000)
Doctorate Biosystems Science and Engineering (639000)
Doctorate Earth Sciences (664002)
Doctorate Earth Sciences ETH-UZH (665000)
Doctorate Earth Sciencess UZH-ETH (665100)
Doctorate Environmental Sciences (739002)
Doctorate Agricultural Sciences (739102)
Doctorate Humanities, Social & Political Sciences (864002)

Offered in

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