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

Start of Lectures: Wednesday, September 19, 2012.

Start of Exercises: Friday, September 28, 2012.

Grading Policy: 

A NUMERICAL GRADE for the course is based only on the written end-of-Semester final examination.
Participation in the written end-of-Semester final examination requires a ''TESTAT''.
A ''TESTAT'' constitutes of ''successful participation in course''.
It is NOT a numerical grade. The ''TESTAT'' is given if correct solution of at least 70 per cent of COURSE HOMEWORK ASSIGNMENTS has been achieved.

Students wishing to view their corrected exam are invited to visit us on Wednesday, February 20th, 2013, between 12:00 and 14:00. Room: HG J47

VVZ-Link

Examination Details:

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
under WINDOWS. An own computer is NOT allowed for the examination.

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

Exercises

The details concerning the exercise classes can be found here.

Prerequisites

• Mandatory:
  Measure Theory, Elementary Probability, Probability Theory I, MATLAB programming
• Recommended: course on
  Stochastic Processes

Lecture notes

Lecture notes will be handed out in class.

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.