Methods of Monte Carlo Simulation II

Dr. Tim Brereton

Teaching assistant
Matthias Neumann

Time and Place

Friday, 10-12 am (220, Helmholtzstr. 18)

Excercise session
Thursday, 1 - 2 pm (220, Helmholtzstr. 18)


 2 hours lecture and 1 hour excercise

Credit points:4 lecture only
6lecture and reading course


Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik". In particular, the course Methods of Monte Carlo Simulation (winter term 2013/14) is not required.

Intended Audience

Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"

Students from other fields (in particular Physics, Computer Science or Chemistry) are welcome as well; the respective examination board (Prüfungsausschuss) decides on the possible recognition of examinations.


This course is not a sequel to Methods of Monte Carlo Simulation I (MMCS1), but rather a complimentary course. As such, MMCS1 is not a required prerequisite.

In MMCS1, we considered generic Monte Carlo methods for efficiently solving estimation and optimization problems. In this course (MMCS2), we instead focus on simulating probabilistic objects, including many important stochastic processes and structures.

No prior knowledge of these probabilistic objects will be assumed. They will be introduced and some key properties will be examined. We will focus on efficiently generating replicates of these on a computer and using these replicates to solve a number of interesting problems.

Some of the objects we will consider are: stochastic processes that model the movement of particles and the evolution of stock prices; point processes that can model the distribution of a particular type of tree in a forest or the number of defaults in a portfolio of bonds; and spatial random objects that can model magnetization or the distribution of yearly rainfall in various regions of Germany.

This course would be ideal for students interested in learning about applied stochastic modeling.

Reading Course

Students may choose if they want to take a reading course (in addition to the lectures) in order to gain 6 credit points instead of 4.

For the reading course, students will have to study some additional material (which will not be covered in class). The material to read will be announced in the lectures / exercises and will be provided online each week. Moreover, the participants of the reading course will have to write an extended exam, which will cover this additional material.

The first reading is here:

Reading 1

Reading 2


The answer to the question in the exercises will be discussed at 12:30 on Thursday (immediately before the exercises).

Requirements and Exam

In order to participate in the final exam, it is necessary to earn 50% of the points on all problem sheets. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.

Time and place

First exam: August 9, 9.30 am (N24, H12)

Second exam: October 7, 2.00 pm (N24, H15)

For the exams you will NOT be allowed to bring any notes. Moreover, calculators are not permitted (you won't need one).


The exam is corrected!

You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in the following tabular:

Mark   Points
1,048 - 46
1,345.5 - 44
1,743.5 - 41.5 
2,041 - 39
2,338.5 - 36.5
2,736 - 34
3,033.5 - 31.5
3,331 - 29
3,729 - 26.5
4,026 - 24

0 - 23.5

The second exam is corrected!

You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in the following tabular:

Mark  Points  
1,052 - 49
1,348.5 - 46.5
1,746 - 44 
2,043.5 - 41.5
2,341 - 39
2,738.5 - 36.5
3,036 - 34
3,333.5 - 31.5
3,731 - 29
4,028.5 - 26

25.5 - 0

Problem Sheets

In order to receive points for your problem sheets, a registration at SLC is required.

Exercise Sheet 01

Exercise Sheet 02

Exercise Sheet 03

Exercise Sheet 04

Exercise Sheet 05

Exercise Sheet 06

Exercise Sheet 07

Exercise Sheet 08

Exercise Sheet 09

Exercise Sheet 10

Exercise about reading material 2

Solution 01

Matlab Solution 02

Matlab Solution 03

Matlab Solution 04

Matlab Solution 05

Matlab Solution 06

Matlab Solution 07

Matlab Solution 08

Matlab Solution 09

Matlab Solution 10

Matlab Solution (Reading 2)

Lecture Notes

Lecture notes will be provided roughly one week after the correpsonding lectures.

The lecture notes are here:

Lecture notes


Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.

Brémaud, P. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 1999.

Cont, R. and P. Tankov. Financial Modeling with Jump Processes. Chapman & Hall/CRC, 2003.

Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2004.

Graham, C. and D. Talay. Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation. Springer, 2013.

Kroese, D. P., T. Taimre and Z. Botev. Handbook of Monte Carlo Methods. Wiley, 2011.

Møller, J. and Waagepetersen, R. P. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, 2003.

Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.

Winkler, G. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer, 2003.



Teaching assistant


The post-exam review will take place on Thursday, August 14 from 2 to 3 pm in Dr. Brereton's office (room 1.43 in Helmholtzstr. 18)

The exam will take place in N24, H12.

Lecture notes updated

The exam section has been updated. In particular, you will not be allowed to bring any notes or calculators.

Please register for the prerequisites at the LSF-portal. Prerequisites for the exam without reading course have the number 13269, while prerequisites for the exam including the reading course have number 13325.

Lecture notes have been updated.