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.
Contents
- 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
Prerequisites
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
Exercises
See page iv of the lecture notes (updated weekly).
In addition, we also expect you to submit your .m-file at https://people.math.ethz.ch/~grsam/submit/?VL=02.
Literature
- 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.