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401-4657-00L 6 Credits BSC , DR , MSC D-MATH
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Numerical Analysis of Stochastic Ordinary Differential Equations

Lecturers & Examiners: Dr. Diyora Salimova
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
VVZ CR n/a

Last Updated: 2026-02-05 15:34:47

Abstract

Course 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.

Objective

The 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.

Content

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 Applications to computational finance: Option valuation

Resources

Lecture Notes

There will be English, typed lecture notes for registered participants in the course.

Literature

P. 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.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , DR , MSC
Frequency
Yearly recurring

Examination

Type
end-of-semester examination
Digital
The exam takes place on devices provided by ETH Zurich.
Learning 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.

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
The lecturers will communicate the exact lesson times of ONLINE courses
  • Mon 16:00-18:00 (ON LI NE)
  • Wed 14:00-15:00 (ON LI NE)
3 h weekly
exercise Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
Groups are selected in myStudies. Responsible lecturer: Dr. D. Salimova The lecturers will communicate the exact lesson times of ONLINE courses.
  • Wed 15:00-16:00 (ON LI NE)
  • Wed 15:00-16:00 (ON LI NE)
1 h weekly

Offered In