Financial Mathematics I

Lecture Winter Term 2015/2016

Financial Mathematics I


Alexander Lindner

Class and Tutorial Teacher:

Dirk Brandes


MSc Finance: Compulsory Course  

Bachelor/Master Mathe: Wahlpflichtmodul im Bereich Angewandte Mathematik 
Bachelor WiMa: Wahlplichtmodul im Bereich SOF 
Master WiMa: Pflichtmodul 




You can collect the DAV certificate in the office of Martha Moritz, Helmholtzstr. 20, room 1.67.

Those of you, who participate in the exam for the DAV certificate, go to room H14 if your last name begin with A-H.

Those of you, who participate in the exam for the DAV certificate, go to room H16 if your last name begin with I-N.

All others, i.e. those, who just write the normal exam and those, who write the DAV Certificate but your last name begins with O-Z, go to room H4/5.


On Tuesday, 2nd of February, there will be a practitioners talk given by Dr. Christian Hering and Dr. Mario Römer from the LBBW instead of the lecture.

On Friday, 5th of February, there is an exercise class instead of a lecture, whereas on Thursday, 11th of February, there is an exercise class instead of the lecture.

On Thursday, 21st of January, there is an exercise class instead of a lecture, whereas on Friday, 22nd of January, there is a lecture instead of the exercise class.

The exercise class on Friday, 4th of December, is omitted.

We offer a second tutorial course for the Master of Finance students, especially those for whom the time on Wednesday clashes with Risk Management in Insurance, every Friday at 14:15 p.m. in room 120, Helmholtzstr. 18, starting on the 20th of November.

On the 18th of November, the tutorial course again takes place in room E20, Helmholtzstr. 18.

We offer one hour tutorial course for the master of finance students before the regular start on Wednesday, 28th of October, in room E20, Helmholtzstr. 18.

For the lecture to provide information and the exercise sheets, we are using Moodle. The password you need to enter the course was given to you in the first lecture.

The DAV supplement takes place on every Tuesday and Thursday between 03/11/2015 and 26/11/2015,

18:00 - 19:30, N24-H14. For more details and future information see DAV Supplement.



Time and Venue:

Lecture: Tuesday, 14.15-16, N25-H3; Thursday, 12.15-14, N25-H3;

First Lecture: 13/10/2015;

Exercise Course: Friday, 10.15-11.45, N24-H12;

First Exercise Classes: 23/10/2015;

On 16/10/2015 a lecture will be given instead of the exercise class.

Solutions of the first exercise sheet: 23/10/2015

Tutorial (only MSc Finance students): Wednesday, 14-16, N25-H9

First tutorial: 04/11/2015.



Final Exam:

written, Tuesday the 23.02.2016 at 08:15 (the DAV part starts at 10:15) in N25-H4/5 N24-H14, N24-H16, and O23-2619.

written (retake), Tuesday the 05.04.2016 at 10:15 in N25-H3 and N25-H4/5 (no possibility to get the DAV certificate).

The Financial Mathematics I exam is open. That means that you can chose the date at which you want to write the exam. Note that, if you want to write also the DAV part, you have to write the exam on the 23rd of February 2016.

Prerequisite: 50% of exercise points.

To participate in the final exam, you have to register first for the precourse (Vorleistung) at until February 5th 2016. 

Afterwards we will enter whether you have passed the precourse or not in the system. If you have passed the precourse, you can register for the Financial Mathematics I exam until February 19th 2016. If you miss to register for either the precourse or the exam, you cannot attend the final exam.

Authorized Auxiliaries (FiMa I):

  • a non-programmable calculator (no smartphone),
  • one A4 sheet or equivalent 2 pages of handwritten notes,
  • a permanent pen.

Authorized Auxiliaries (DAV-Part):

  • a non-programmable calculator (no smartphone),
  • a permanent pen.



Analysis I+II; Lineare Algebra I+II; Stochastik I; Elementary Probability, Statistics and Measure Theory or Introduction to Measure Theoretic Probability (can be attended in the same winter term, beginning on 05/10/2015).



This course covers the fundamental principles and techniques of financial mathematics in discrete- and continuous-time models.  Specific topics are

  • Financial market models in discrete time: arbitrage freeness and completeness     
  • Conditional expectation and discrete time martingales
  • Valuation of European, American and path-dependent options
  • Foundations of continuous time market models and of the Black-Scholes
  • Interest rate models and derivatives
  • Risk measures
  • Portfolio optimisation and CAPM

  • A. Irle, Finanzmathematik: Die Bewertung von Derivaten, Vieweg + Teubner 2012.
  • N.H.Bingham & R.Kiesel, Risk Neutral Valuation (2nd edition), Springer 2004.
  • H. Föllmer & A. Schied, Stochastic Finance: An introduction in discrete time, de Gruyter, 2004.
  • P.K. Koch & S. Merino: Mathematical Finance and Probability: A Discrete Introduction, Springer 2013.
  • Musiela, M.; M. Rutkowski: Martingale methods in financial modelling. (Springer, New York), 2nd ed. 2004.
  • S. Shreve, Stochastic Calculus for Finance I: The  Binomial Asset Pricing Model, Springer, 2004.
  • S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.

Exercise sheets:               


Can be downloaded on Moodle.


Lecture notes:

Lecture Notes