Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin. I: Monte Carlo Methods)

General information

What Who/When Where What Who/When Where
Lecturer: Prof. Dr. Arnulf Jentzen   Coordinators: Ryan Kurniawan  
        Timo Welti  
Lecture: Wed, 13:00-15:00 HG E1.1 Exercises: Thu, 14:00-15:00 or HG E1.1
  Fri, 13:00-14:00 HG E1.1   Fri, 12:00-13:00 HG E1.1
      Office Hour: Mon, 14-15 HG G53.x
        or write an email to the coordinators for an appointment  
First lecture: Wed, 21.09.2016   First exercise series: Fri, 30.09.2016  
      First exercise classes: Thu, 13.10.2016 (A-Ma) HG E1.1
        Fri, 14.10.2016 (Mo-Z) HG E1.1
End-of-Semester-Exam: Wed, 21.12.2016, 12:30-14:30 HG E19 Exam inspection: Tue, 28.02.2017, 12:15-13:15 HG D3.1

Examination Details

A NUMERICAL GRADE for the course is based only on the written end-of-Semester final examination.

The 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. An own computer is NOT allowed for the examination.

Date of the End-of-Semester examination: Wednesday, December 21, 2016, 12:30-14:30; students must arrive before 12:00 at ETH HG E19.

Room for the End-of-Semester examination: ETH HG E19.



  • 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


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

  • Mandatory courses: Elementary Probability, Probability Theory I
  • Recommended courses: Stochatic Processes

Lecture notes

The pdf file can be downloaded from the link below.

Lecture notes                         Version: December 14, 2016


See page iv of the lecture notes (updated weekly).

In addition, we also expect you to submit your .m-file at



  • P. Glassermann, Monte Carlo Methods in Financial Engineering, Springer Publ. 2004.
  • P.E. Kloeden & E. Platen, Numerical Solution of Stochastic Differential Equations, Springer Publ. 1992.