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401-4657-DRL 3 Credits DR D-MATH
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Numerical Solution of Stochastic Ordinary Differential Equations

Lecturers & Examiners: Dr. Andreas Stein
Alternative course titles: "Numerical Analysis of Stochastic Ordinary Differential Equations" / "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to with their name, course number and student ID. Please see
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Last Updated: 2026-02-05 16:02:04

Abstract

This course is on the numerical approximations of stochastic ordinary differential equations (SDEs) driven by Brownian motions and Lévy processes. SDEs have several applications, for example in financial engineering.The contents cover stochastic processes, stochastic calculus, well-posedness results for SDEs, strong and weak approximations of SDEs, and simulation via Monte Carlo methods.

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

Brownian motion and Lévy processes Stochastic integration and stochastic calculus Stochastic ordinary differential equations (SDEs) Numerical approximations of SDEs Stochastic simulation and Monte Carlo methods Applications to computational finance: Option valuation

Resources

Lecture Notes

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

Literature

P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. D. Applebaum: Lévy Processes and Stochastic Calculus. Cambridge University Press, 2009.

General Information

Language
English
Levels
DR
Frequency
Yearly recurring

Examination

Type
ungraded semester performance
Meaningful solutions to 70% of 11 weekly homework assignments are required to obtain credits for this course.

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 Solution of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
  • Mon 16:15-18:00 (HG D 1.2)
  • Wed 14:15-15:00 (HG D 5.2)
3 h weekly
exercise Numerical Solution of Stochastic ODEs (Comp. Meth. Quant. Fin.: Monte Carlo and Sampling Methods)
  • Wed 15:15-16:00 (HG D 5.2)
  • Wed 15:15-16:00 (LFW C 1)
1 h weekly

Offered In