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

SemesterHerbstsemester 2019
DozierendeK. Kirchner
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarAlternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"



Katalogdaten

KurzbeschreibungCourse 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.
LernzielThe 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.
InhaltGeneration 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
SkriptThere will be English, typed lecture notes for registered participants in the course.
LiteraturP. 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.
Voraussetzungen / BesonderesPrerequisites:

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.

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte6 KP
PrüfendeK. Kirchner
FormSemesterendprüfung
PrüfungsspracheEnglisch
RepetitionDie Leistungskontrolle wird nur am Semesterende nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich.
Zusatzinformation zum PrüfungsmodusLearning 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.

Lernmaterialien

 
HauptlinkCourse webpage
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Lehrveranstaltungen

NummerTitelUmfangDozierende
401-4657-00 VNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)3 Std.
Mo15-17HG D 1.2 »
Mi13-14HG E 1.1 »
K. Kirchner
401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
Gruppeneinteilung erfolgt über myStudies.
1 Std.
Mi14-15HG D 7.1 »
14-15HG E 1.1 »
K. Kirchner

Gruppen

401-4657-00 UNumerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
GruppenG-01
Mi14-15HG D 7.1 »
G-02
Mi14-15HG E 1.1 »

Einschränkungen

Keine zusätzlichen Belegungseinschränkungen vorhanden.

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